blLH 


A,  CR^WTHER 


TEXT -BOOKS  OF  CHEMICAL  RESEARCH  AND   ENGINEERING. 


MOLECULAR    PHYSICS 


BY 


JAMES    ARNOLD    CROWTHER,    M.A. 

FELLOW    OF   ST.    JOHN'S    COLLEGE,    CAMBRIDGE,    AND    DEMONSTRATOR 
IN    PHYSICS   AT   THE    CAVENDISH    LABORATORY 


PHILADELPHIA 

P.   BLAKISTON'S   SON    &   CO. 

1 01 2    WALNUT    STREET 
1914 


PREFACE 

THE  present  volume  is  an  attempt  to  give  a 
connected  account  of  the  constitution  and  properties 
of  the  atom  and  molecule  in  the  light  which  has 
been  thrown  upon  these  particles  by  recent  physical 
research.  From  the  great  mass  of  experimental 
observations  which  constitute  what  has  been  called 
somewhat  vaguely  the  "  New  Physics "  I  have 
endeavoured  to  select  those  portions  which  have 
a  direct  bearing  on  this  important  and  fascinating 
subject,  and  I  have  drawn  freely  on  all  available 
sources  of  information,  some  of  which  are  indicated 
in  the  Bibliography  at  the  end  of  the  book. 

To  Professor  Sir  J.  J.  Thomson  I  owe  a  debt  of 
gratitude  for  his  kindness  in  allowing  me  to  select 
from  his  experimental  negatives,  and  to  reproduce, 
the  Positive  Ray  photographs  which  illustrate 
Chapter  IV.  I  owe  him  still  more  for  the  privilege 
which  I  have  enjoyed  during  the  past  eight  years  in 
the  Cavendish  Laboratory,  of  moving  in  daily 
contact  with  much  of  the  work,  and  of  drinking  in, 
as  it  were  at  the  fountain  head,  much  of  the  theory 
narrated  in  the  present  volume.  To  this  must  be 
ascribed  any  merits  which  the  following  pages  may 
be  found  to  possess  ;  for  their  errors  and  deficiencies 
I,  alone,  am  responsible. 

J.A.C. 


294689 


CONTENTS 


CHAPTER  I. — INTRODUCTION    .....          i 
Historical  survey.     The  old  and  the  new  physics. 
The    molecular    theory    of    matter.     Molecular 
magnitudes. 

CHAPTER  II. — THE  PHYSICS  OF  THE  ELECTRON  .  10 
The  discharge  of  electricity  through  gases. 
Cathode  rays.  Measurement  of  the  ratio  of 
the  mass  to  the  charge  for  the  cathode  rays. 
Measurement  of  the  charge  on  an  electron. 
Photography  of  the  tracks  of  ionizing  particles. 

CHAPTER  III. — THE  POSITIVE  PARTICLE  .      •    .       34 

The  a-particles  from  radio-active  substances. 
Counting  the  a-particles.  The  charge  on  an 
a-particle.  Production  of  helium  from  a-rays. 

CHAPTER  IV. — THE  NEW  METHOD  OF  ANALYSIS  .  42 
Positive  particles  in  the  discharge  tube.  Sir  J.  J. 
Thomson's  experiments.  Measurement  of  the 
velocity  and  mass  of  the  positive  particles.  Posi- 
tive ray  analysis.  The  new  gases.  Application 
of  the  method  to  the  study  of  chemical  decom- 
position. Electrical  methods  of  measurement. 

CHAPTER  V. — THE  NATURE  AND  SIZE  OF  AN  ELECTRON  67 
The  Faraday  tubes.  Electromagnetic  mass. 
Variation  of  electromagnetic  mass  with  speed. 
Kaufmann's  experiments  on  the  y8-rays  from 
radium.  The  radius  of  an  electron.  The  num- 
ber of  electrons  in  the  atom.  The  electron  theory 
of  matter. 

CHAPTER  VI. — THE  CHEMISTRY  OF  THE  MODEL  ATOM       86 
"  Model "    atoms.     The    stability    of   groups    of 
electrons.     Cohesion  and  adhesion.     The  periodic 
law.     The  electron  theory  of  valency.     Valency 
and  the  dispersion  of  light. 


viii  CONTENTS 

PAGE 

CHAPTER  VII. — THE  ATOM  IN  VIBRATION         .          .in 
Propagation    of   disturbances   along   a    Faraday 
tube.     The  wave  theory  of  light.     The  Zeeman 
effect.     Spectral  series.     The  origin  of  spectra. 

CHAPTER  VIII. — THE  MOLECULAR  THEORY  OF  MATTE.R     131 
Solids,  liquids,  and  gases.     The  kinetic  theory  of 
heat.     Change  of  state.     Van  der  Waal's  equa- 
tion.    The  size  of  the  atom.     Electron  theory  of 
thermal  and  electrical  conduction. 

CHAPTER  IX. — THE  ATOM  IN  DISSOLUTION      .          .147 
Radioactive  transformations .    The  decomposition 
of     an     element.       Radio-activity    of    ordinary 
materials.     Conclusion. 

APPENDIX  A. — DEFLECTION  OF  THE  POSITIVE  RAYS  160 
APPENDIX  B. — ELECTRO-MAGNETIC  MASS  .  .161 
APPENDIX  C. — THE  ZEEMAN  EFFECT  .  .  .163 
TABLE  OF  ATOMIC  DATA  .  .  .  .  165 

BIBLIOGRAPHY        .          .          .          .  .          .     166 


MOLECULAR    PHYSICS 


CHAPTER  I. 
INTRODUCTION. 

THE  history  of  the  rise  of  molecular  theory  has 
often  been  written.  From  Dalton,  who  first  gave 
to  the  conceptions  of  the  early  atomists  a  definite 
meaning  and  a  real  experimental  basis,  through 
Avogadro  and  his  fertile  hypothesis  of  the  molecule, 
and  so  on  to  the  kinetic  theory  of  Clausius  and  Max- 
well, the  story  is  told  in  almost  every  text-book  of 
Chemistry  and  Physics,  and  is  familiar  as  household 
words  to  all  their  readers.  Here  for  a  time  science 
seemed  to  pause  in  her  progress.  It  seemed  as  if  the 
memoirs  of  these  brilliant  mathematicians  were  to 
contain  the  last  word  in  molecular  theory. 

If  this  had  been  so,  the  following  pages  would 
have  been  superfluous.  In  the  last  few  years,  how- 
ever, new  fields  have  been  opened  to  the  student  of 
molecular  phenomena ;  new  methods  of  approach 
have  been  evolved  so  potent  in  character  that  sub- 
jects about  which  we  had  until  then  barely  sufficient 
grounds  for  speculation  are  now  laid  open  to  direct 
experimental  attack.  The  molecule  has  been  raised 
from  a  conception  only  realisable  experimentally  in 
millions  to  the  rank  of  a  definite  particle  whose  entry 
into  our  apparatus  produces  a  definite  and 
measurable  effect.  At  the  same  time  the  accuracy, 

M.P.  I 


.2  MOLECULAR  PHYSICS 

1  \  "  '•    •>  *^c  -*s-frc"^' 

and  what  is  still  more  important,  the  certainty,  of  our 
measurements  of  molecular  magnitudes  have  been 
enormously  increased.  It  seemed,  therefore,  neither 
undesirable  nor  devoid  of  interest  to  attempt  to 
re- write  the  subject  of  molecular  physics,  not  from 
the  standpoint  of  the  kinetic  theory,  by  which  it  was 
approached  historically,  and  which  constituted  for 
many  years  the  sole  line  of  attack,  but  rather  in  the 
light  thrown  upon  these  problems  by  the  recent 
developments  in  what  has  come  to  be  known  as  the 
"  New  Physics/' 

In  order  to  fix  our  attention  upon  the  problems 
to  be  dealt  with,  and  to  recall  to  our  minds  some 
clear  ideas  of  the  magnitudes  with  which  we  shall 
have  to  deal,  it  may  be  well  to  consider  briefly  the 
position  to  which  we  had  been  brought  by  the 
exponents  of  the  kinetic  theory. 

The  atom  itself  was  a  purely  chemical  conception. 
It  took  its  rise  in  an  attempt  to  explain  the  laws  of 
chemical  combination,  and  represents  the  smallest 
mass  of  an  element  which  can  take  part  in  a  chemical 
reaction.     By  its  first  exponents  it  was  regarded  as 
homogeneous  and  indivisible.     This  view  is  no  longer 
held.     We  shall  see  later  that  we  must  conceive  of 
the   atom   as  something   approaching  a  planetary 
system  on  an  infinitesimal  scale.     A  study  of  the 
phenomena  of  radioactivity  has  driven  us  to  believe 
that  in  them  we  are  dealing  with  a  true  decompo- 
sition of  a  true  chemical  atom  ;    that  the  element 
radium  is  in  fact  a  decomposition  product  of  the 
atom  of  uranium,   and  is  itself  in  the  course  of 
transition  into  an  atom  of  lead,  with  the  emission 
during  the  process  of  several  atoms  of  helium.     This 
break  up  of  an  atom,  however,  is  a  process  which  we 
are  permitted  to  watch,  but  not  to  control.     So  far 
we  have  not  succeeded  in  either  accelerating  or 
retarding  its  progress  in  any  way  whatever. 

In  compounds  the  atoms  of  the  different  elements 


INTRODUCTION  3 

were  supposed  to  be  grouped  together  into  similar 
particles  or  molecules,  the  ratio  of  the  masses  of  the 
components  being  the  same  in  each  individual  mole- 
cule as  in  the  compound  as  a  whole.  It  was  soon 
found  necessary  to  assume  that  even  in  the  elements 
the  atoms  were  usually  connected  into  groups  of  two 
or  more  to  form  a  larger  particle,  which,  unless  taking 
part  in  a  chemical  reaction,  always  moved  and  acted 
as  a  single  system.  This  extension  of  the  theory  was 
due  to  Avogadro,  and  his  additional  hypothesis  that 
the  number  of  these  molecules  in  a  given  volume  of 
gas  under  similar  conditions  is  independent  of  the 
nature  of  the  gas  was  the  first  great  generalisation 
in  the  physics  of  the  molecule. 

It  was  soon  realised  that  these  molecules  were 
particles  exceedingly  small  in  size.  Various 
attempts  to  determine  the  approximate  diameter  of 
the  molecules  all  led  to  the  result  that  it  was  not  very 
much  greater  than  2  X  io~8  cms.  Various  illustra- 
tions have  been  employed  to  assist  us  to  grasp  the 
extreme  minuteness  of  this  quantity.  If,  for 
example,  a  drop  of  water  were  to  be  magnified  to  the 
size  of  the  earth  the  molecules  in  it  would  be  of  the 
size  of  footballs.  Or  again,  as  a  recent  writer  has 
suggested,  we  may  say  that  the  carbon  atom  in  the 
printed  page  subtends  at  the  reader's  eye  the  same 
angle  as  would  be  subtended  there  by  a  man  on  the 
moon. 

The  number  of  molecules  in  any  visible  portion 
of  matter  is,  of  course,  correspondingly  large. 
According  to  the  latest  determinations  the  number 
of  molecules  in  I  cub.  cm.  of  air  under  normal 
conditions  (o°  C.  and  760  mm.  pressure)  is  2*7  X  io19. 
It  is  almost  hopeless  to  attempt  to  conceive  this 
inconceivable  swarm  of  particles.  It  may,  perhaps, 
be  of  some  assistance  to  point  out  that  in  the  highest 
attainable  vacua,  when  the  pressure  of  the  gas  is  not 
more  than  TQOOO  mm*  °f  mercury,  the  number  of 

i — 2 


4  MOLECULAR   PHYSICS 

molecules  present  in  every  cubic  millimetre  of  the 
space  still  exceeds  2,000,000,000. 

In  a  solid  body  we  must  regard  the  molecules  as 
relatively  fixed.  They  are  indeed  in  rapid  vibration 
about  their  mean  position,  such  vibration  consti- 
tuting the  phenomenon  which  we  know  as  heat. 
The  fact  that  ancient  gems  and  coins  have  come 
down  to  us  through  many  ages  still  preserving  their 
sharp  outlines  and  their  beautiful  and  clear-cut 
engraving  shows  that,  in  the  absence  of  external 
forces,  the  defection  of  a  molecule  in  a  solid  from  its 
original  station  must  be  of  exceedingly  rare 
occurrence. 

In  liquids,  however,  we  must  regard  the  molecules 
as  free  to  move.  A  liquid  has  no  definite  shape  of 
its  own,  and  two  liquids  if  left  quite  undisturbed  will 
gradually  diffuse  through  each  other  with  a  velocity 
which  is  in  general  small  but  quite  measurable.  The 
different  molecules  possess  sufficient  energy  to  escape 
from  the  attraction  of  neighbouring  systems,  but 
move  only  a  very  short  distance  through  the  thickly- 
crowded  space  before  becoming  entangled  in  other 
clusters. 

Gases  differ  from  liquids  in  the  fact  that  the  space 
occupied  by  a  given  number  of  molecules  is  very 
much  greater  ;  and  a  molecule  therefore  travels 
much  further  before  coming  into  collision  with  other 
molecules.  Thus  a  gramme  of  water  substance  when 
transformed  into  steam  occupies  i, 600  times  the 
volume  which  it  had  in  the  liquid  state.  The  mole- 
cules are  therefore  J// 1,600  or,  say,  12  times  as  far 

apart  in  the  gas  as  in  the  liquid.  The  actual  volume 
of  the  molecules  themselves  is  thus  only  a  very  small 
fraction  of  the  volume  filled  by  the  gas,  the  mole- 
cules occupying  the  space  between  their  boundaries 
not  by  filling  it  with  their  bulk,  but  by  moving  about 
in  it  in  all  directions  with  considerable  velocities. 
The  tendency  of  a  gas  to  spread  through  the  whole 


INTRODUCTION  5 

of  the  space  accessible  to  it  thus  represents  the 
tendency  of  each  molecule  to  proceed  'on  its  path  in 
a  straight  line  when  not  opposed  by  any  obstacle, 
while  the  pressure  on  the  boundaries  of  the  gaseous 
space  is  due  to  the  exceedingly  rapid  series  of  impacts 
made  on  them  by  the  innumerable  swarm  of  mole- 
cules in  motion. 

The  velocity  with  which  the  molecules  in  a  gas 
are  moving  can  easily  be  calculated  when  the  pressure 
and  density  are  known.  The  mean  velocity  of  a 
molecule  of  oxygen  at  the  freezing  point  of  water  is 
about  425  metres  per  second,  or  about  1,000  miles  per 
hour.  It  is,  therefore,  somewhat  greater  than  the 
velocity  of  sound  through  air  under  the  same  con- 
ditions (331  metres  per  second).  In  addition  to 
collisions  upon  the  boundaries  each  molecule  collides 
from  time  to  time  with  other  molecules  of  the  gas, 
the  number  of  collisions  made  by  a  single  molecule 
under  ordinary  conditions  of  temperature  and 
pressure  being  about  6,000,000,000  every  second. 

The  distance  travelled  by  the  particle  between 
two  collisions  is  known  as  its  free  path.  Its  actual 
value  between  any  two  collisions  depends,  of  course, 
upon  chance.  Its  mean  value  can,  however,  be  cal- 
culated from  the  viscosity  of  the  gas.  For  air  under 
ordinary  conditions  it  is  about  7*6  X  lo™6  cms..,  or 
roughly  Too§ooo  of  an  inch- 

This  mean  free  path,  although  a  giant  among 
molecular  magnitudes,  is  still  rather  smaller  than  the 
smallest  distance  we  may  ever  hope  to  perceive. 
Abbe  has  shown  that  two  objects  would  have  to  be 
separated  by  rather  more  than  twice  this  distance 
before  they  could  be  resolved  by  the  best  possible 
microscope  working  under  the  best  conditions. 

The  mass  of  each  molecule  is,  of  course,  exceed- 
ingly minute  ;  according  to  the  recent  determina- 
tions of  Rutherford,  which  we  shall  describe  later,  the 
mass  of  a  hydrogen  atom  is  i'6i  X  io~24  gms.,  a 


6  MOLECULAR  PHYSICS 

number  so  minute  that  it  can  hardly  be  said  to  con- 
vey to  the  mind  any  impression  at  all.  This  number, 
it  will  be  seen,  represents  the  value  in  grammes  of 
the  chemical  unit  of  atomic  weight  ;  the  mass  in 
grammes  of  any  atom  or  molecule  can  thus  be  calcu- 
lated from  a  table  of  atomic  weights  by  merely 
multiplying  the  chemical  atomic  or  molecular  weight 
by  this  factor.  Small  as  is  this  quantity  we  shall  see 
that  its  value  is  known  with  certainty  to  within  a 
very  few  per  cent. 

Of  the  quantities  with  which  we  have  been  deal- 
ing, the  kinetic  theory  gave  accurately  the  velocity 
of  the  molecule  and  the  mean  free  path.  It  threw 
only  a  dim  and  somewhat  uncertain  light  upon  the 
number  and  mass  of  the  individual  molecules.  As 
to  the  nature  of  the  molecule  it  can  hardly  be  said  to 
have  given  any  information  at  all.  It  is  at  once  the 
strength  and  the  weakness  of  the  statistical  methods 
employed  in  the  kinetic  theory,  that  given  a 
sufficiently  large  number  of  molecules,  their  exact 
number,  size,  mass  and  properties  become  for  many 
purposes  matters  of  indifference.  Thus  many  of  the 
properties  of  gases  were  successfully  deduced,  in  the 
first  place,  on  the  assumption  that  the  molecule  was 
a  hard  sphere,  an  assumption  which  in  the  case,  say, 
of  a  molecule  like  that  of  oxygen  built  up  of 
two  atoms  is  almost  certainly  incorrect.  It  will  be 
seen  then  how  little  light  can  be  thrown  upon 
the  individual  molecule  by  investigations  of  this 
nature. 

As  the  moleeule  itself  lay  far  beyond  the  limits  of 
vision,  and  as  the  kinetic  theory  could  afford  so  little 
certain  information,  it  might  have  seemed  that  we 
must  rest  content  with  the  knowledge  already 
attained.  Speculation  as  to  the  nature  of  the  atom 
was  not  wanting,  ranging  from  the  simple  hard  atom 
of  the  original  theory  to  the  centre  of  force,  of 
Boscovitch,  and  the  vortex  atom  of  Professor 


INTRODUCTION  7 

Thomson,  the  early  speculation  of  one  who  has  done, 
perhaps,  more  than  any  other  to  render  possible  a 
true  theory  of  the  atom.  These  theories,  ingenious  as 
they  were,  withered  for  lack  of  experimental  support, 
and  the  subject  became  gradually  to  be  regarded  as 
being  in  the  realm  of  the  unknowable.  Meanwhile 
the  great  success  of  the  statistical  methods  of  the 
kinetic  theory,  the  extension  of  thermodynamics,  and 
the  study  of  phenomena  from  a  consideration  of 
their  equilibrium  conditions  which  followed  on  the 
work  of  Willard  Gibbs,  were  leading  further  and 
further  away  from  atomic  and  molecular  hypotheses. 
Fortunately  one  loophole  remained  into  this 
region  of  the  infinitely  small.  The  kinetic  energy 
of  a  particle  is  equal  to  the  product  of  one-half  its 
mass  into  the  square  of  its  velocity.  However  small 
the  mass  of  the  particle,  therefore,  we  can  theoreti- 
cally by  sufficiently  increasing  its  velocity  endow  it 
with  an  appreciable  amount  of  energy.  In  the  case 
of  a  molecule  the  velocity  required  will,  of  course,  be 
very  large.  The  energy  of  a  molecule  in  the  air 
under  normal  conditions  of  temperature  and  pressure 
is  about  5  X  io~~u  ergs,  assuming  the  mass  and 
velocity  already  given.  This  is  far  too  small  to  be 
detected.  Let  us  suppose,  however,  that  we  can 
endow  our  molecule  with  a  velocity  much  greater 
than  this,  approaching  2  X  io9  cms.  per  second.  The 
energy  of  an  oxygen  molecule  moving  with  such  a 
speed  would  be  J  (32  X  i'6i  X  io~24)  .  (2  X  io9)2  ergs, 
or  about  io~4  ergs.  This,  though  small,  is  not  less 
than  can  be  appreciated  in  other  forms  of  energy. 
Thus  Lord  Rayleigh  has  estimated  that  the  faintest 
sound  which  can  be  heard  transmits  every  second 
across  a  square  centimetre  of  area  at  right  angles  to  its 
path  about  2*3  X  io~5  ergs.  The  energy  in  the 
faintest  perceptible  beam  of  light  is  not  far  dif- 
ferent from  this.  Thus  the  energy  of  impact  of  a 
single  molecule  travelling  with  the  velocity  we  have 


8  MOLECULAR   PHYSICS 

suggested  would  be  comparable  with  the  energy  in  a 
faint  beam  of  light  or  a  just  audible  sound. 

The  velocity  ascribed  to  the  molecule  in  this 
calculation  might  seem  impossibly  large.  It  is 
in  fact  about  -^  of  the  velocity  of  light,  and  a 
particle  travelling  with  this  speed  would,  therefore, 
cover  the  distance  from  the  earth  to  the  sun  in  2 
hours.  Such  particles,  however,  actually  exist,  and 
it  is  the  discovery  of  these  particles  and  the  measure- 
ments made  upon  them  that  have  led  to  the  great 
advances  in  molecular  physics  which  we  are  about  to 
describe.  Particles  having  this  velocity  are  shot  out 
in  large  numbers  from  radioactive  bodies.  To 
anticipate  a  little  we  may  say  that  the  a-particles 
from  radium  consist  of  atoms  of  helium  shot  out  with 
a  speed  of  this  order  of  magnitude,  and  bearing  a 
positive  charge.  Thus  it  is  that  a  single  a-particle 
is  able  to  cause  a  flash  of  light  when  it  strikes  upon  a 
screen  covered  with  a  suitable  material. 

The  a-particles  consist  of  helium  atoms  only. 
Velocities  approaching  that  of  the  a-particles  can 
be  given  to  atoms  and  molecules  of  other  substances 
by  passing  an  electric  discharge  through  them  in  the 
gaseous  state  at  very  low  pressures.  The  phenomena 
of  the  discharge  tube  have  indeed  afforded  the  best 
means  of  investigating  the  properties  of  moving 
electrified  particles,  and  we  shall  proceed  to  their 
consideration  immediately. 

In  order  to  complete  our  survey  we  will  anticipate 
so  far  as  to  say  that  the  first  experimental  investiga- 
tion of  these  phenomena  led  to  results  of  a  startling 
nature.  Professor  Sir  J.  J.  Thomson,  as  the  result 
of  a  brilliant  series  of  researches  and  deductions, 
which  may  truly  be  said  to  mark  a  fresh  era  in  the 
progress  of  science,  showed  that  the  most  conspicuous 
set  of  particles  in  the  discharge  tube,  namely,  those 
constituting  the  cathode  rays,  had  a  mass  not  more 
than  7^00  Pai"t  °f  that  of  a  hydrogen  atom. 


INTRODUCTION  9 

It  was  found,  moreover,  that  whatever  the  nature 
of  the  gas  through  which  the  discharge  was  passing, 
whatever  the  nature  of  the  electrodes  used,  the  mass 
of  the  cathode  particle  produced  and  the  magnitude 
of  the  charge  carried  by  it  was  always  the  same. 
These  cathode  particles,  corpuscles  or  electrons,  as 
they  came  to  be  called,  must  thus  be  regarded  as 
forming  an  integral  part  of  the  atom  of  every  kind  of 
substance.  They  are  therefore  even  more  funda- 
mental than  the  atom  itself,  since  they  form  part  of 
the  material  from  which  the  atom  is  built  up.  The 
methods  used  in  their  investigation  are  similar  in 
principle  to  those  which  have  recently  been  applied 
to  atoms  and  molecules,  but  the  special  properties  of 
the  electrons  rendered  their  experimental  investiga- 
tion less  difficult  than  that  of  the  atom  or  molecule, 
so  that  for  a  time  it  could  truly  be  said  that  far  more 
was  known  of  the  electron  than  of  the  atom  itself. 
For  these  reasons  we  will  commence  our  study  of 
molecular  physics  with  the  consideration  of  the 
electron. 


CHAPTER  II. 
THE  PHYSICS  OF  THE  ELECTRON. 

THE  general  appearance  of  an  ordinary  discharge 
tube  is  perhaps  familiar  to  most  of  my  readers.  It 
is  represented  somewhat  diagrammatically  in  Fig.  i. 
Covering  the  cathode  C  is  a  velvety  light  known  as 
the  cathode  glow.  Beyond  this  is  a  comparatively 
dark  space,  named  after  its  discoverer  Sir  William 
Crookes.  If  the  pressure  in  the  tube  is  fairly  high 
this  Crookes  dark  space  will  be  so  close  to  the 
cathode  and  so  small  as  to  be  hardly  visible.  Beyond 


c 

FIG.  i. — THE  DISCHARGE  TUBE. 

this  dark  space  is  another  luminous  area,  the 
negative  glow,  bounded  on  the  side  remote  from 
the  cathode  by  still  another  obscure  area,  the  Faraday 
dark  space.  The  length  of  the  tube  occupied  by 
these  phenomena  depends  mainly  on  the  pressure 
of  the  gas,  and  is  practically  independent  of  the 
size  of  the  tube,  the  remainder  of  which,  however 
long,  is  filled  with  a  bright  light  known  as  the 
positive  column,  which  is  frequently,  though  not 
necessarily,  divided  into  numerous  striae.  It  is  the 


THE   PHYSICS   OF  THE  ELECTRON     n 

light  from  this  positive  column  that  is  generally 
employed  in  the  spectroscopic  examination  of  gases 
in  the  discharge  tube. 

If  the  pressure  is  fairly  low  another  phenomenon 
may  be  distinguished.  Proceeding  normally  from 
the  cathode  and  penetrating  in  straight  lines  across 
one  or  more  of  the  dark  spaces  may  be  seen  faint 
bluish  streams  of  light,  known  as  the  cathode  rays. 
As  the  pressure  is  still  further  reduced  these  rays 
become  relatively  more  and  more  important,  and 
penetrate  further  and  further,  until  finally  they 
fall  upon  the  glass  walls  of  the  discharge  tube, 
exciting  there  a  greenish  phosphorescence.  Mean- 
while the  Crookes  dark  space  has  grown  until  it 
occupies  practically  the  whole  of  the  tube,  the 
remaining  parts  of  the  ordinary  discharge  being 
represented  by  the  glow  on  the  cathode  and  a  single 
patch  of  light  near  the  anode  itself. 

The  nature  of  the  cathode  rays  remained  for 
some  time  in  doubt.  However,  in  1895  Perrin 
showed  that  they  transported  a  negative  charge, 
and  in  the  following  year  Professor  Sir  J.  J.  Thomson 
proved  conclusively  that  they  consisted  of  streams 
of  negatively  charged  particles,  moving  with 
extremely  high  velocities  and  having  a  mass  in  all 
probability  much  less  than  that  of  a  hydrogen 
atom. 

Let  us  continue  for  a  moment  the  study  of  the 
discharge  tube.  It  had  long  been  known  that  if  a 
solid  obstacle  were  placed  in  the  path  of  the  discharge 
a  shadow  of  the  object  was  cast  by  the  cathode  rays 
on  the  opposite  wall  of  the  tube.  It  was  noticed 
that  if  the  obstacle  was  placed  within  the  Crookes 
dark  space  a  shadow  was  also  cast  on  the  cathode. 
That  is  to  say,  there  must  also  be  rays  in  the  tube 
proceeding  in  the  opposite  direction  to  the  cathode 
rays  and  falling  upon  the  cathode  itself.  By  using 
a  perforated  cathode,  as  shown  in  the  diagram. 


12  MOLECULAR  PHYSICS 

these  rays  become  visible  as  faintly  luminous 
streaks  of  light,  coming  from  each  of  the  per- 
forations, and  exciting  a  faint  mauve  phosphor- 
escence where  they  strike  the  walls  of  the  tube. 
These  rays  which  carry  a  positive  charge  and  have 
a  mass  comparable  with  that  of  an  atom,  form  the 
positive  particles  to  which  we  have  already  alluded. 

The  high  velocities  of  these  particles  give  them, 
as  we  have  seen,  sufficient  energy  to  produce 
luminous  effects  when  they  fall  upon  suitable  screens. 
The  additional  fact  that  they  carry  an  electric  charge 
enables  us  to  determine  not  only  the  velocity,  but 
also  the  ratio  of  the  mass  of  the  particles  to  the 
charge  which  they  carry. 

The  general  problem  of  the  motion  of  an  electri- 
fied particle  when  moving  under  the  action  of  electric 
and  magnetic  forces  is  one  of  some  little  complexity, 
though  complete  solutions  have  been  given  by 
various  mathematicians.  Fortunately  the  special 
cases  which  are  required  for  our  present  purpose 
lend  themselves  readily  to  the  simplest  treatment. 

Suppose  that  a  particle  of  mass  m  and  charge  e  is 
moving  with  a  velocity  v  at  right  angles  to  a  magnetic 
field  of  strength  H.  In  one  second  the  charge  e  will 
have  moved  through  a  distance  v  cms.  We  may 
therefore  regard  the  path  of  the  particle  as  a  sort  of 
conductor  v  cms.  long,  carrying  an  electric  current 
whose  strength  is  e.  The  mechanical  force  on  such 
a  conductor  when  placed  in  a  magnetic  field  is  known 
from  the  laws  of  electro-magnetic  induction  to  be 
equal  to  the  strength  of  the  field  multiplied  by  the 
current  and  the  length  of  the  conductor,  that  is  to 
the  product  H  .  e  .  v.  Further,  this  force  is  at  right 
angles  to  the  direction  of  the  current  and  to  the  lines 
of  force  in  the  magnetic  field.  A  little  consideration 
will  show  that  under  these  circumstances  the  path 
of  the  particle  is  changed  from  a  straight  line  to  a 
circle  described  in  a  plane  at  right  angles  to  the 


THE  PHYSICS   OF  THE  ELECTRON  13 

direction  of  the  lines  of  force  in  the  magnetic 
field. 

Let  r  be  the  radius  of  this  circle.  A  particle  of 
mass  -m  moving  round  a  circle  with  a  velocity  v 
exerts  a  centrifugal  force  tending  to  urge  it  away 
from  the  centre  of  the  circle.  The  value  of  this  is 
known  to  be 

m  .  v*/r. 

Now  for  equilibrium  the  force  tending  to  urge  the 
particle  away  from  the  centre  must  equal  the  force 
due  to  the  magnetic  field  tending  to  draw  it  in. 
Thus  we  have 

H  .  e  .  v  =  m  .  v^/r 

M  TT  /       \ 

-  .  v  =  H  .  r         .        .        .     (a) 

Again  the  particle  carries  an  electric  charge.  It 
can  therefore  be  deflected  by  an  electric  field.  Let 
X  be  the  strength  of  the  electric  field.  Then  the 
force  experienced  by  the  particle  is  equal  to  X  .  e  and 
acts  upon  the  particle  in  the  direction  of  the  lines  of 
electric  force.  If  now  we  arrange  our  apparatus 
so  that  the  electric  field  and  the  magnetic  field  are 
at  right  angles  to  each  other,  the  forces  upon  the 
particle  due  to  the  two  fields  will  act  along  the  same 
straight  line,  and  by  properly  adjusting  the  sign  of 
the  electric  field  we  can  make  the  two  forces  oppose 
each  other.  It  will  then  be  possible  to  find  a  value 
for  the  electric  field  such  that  the  two  forces  just 
neutralise  each  other  and  the  particle  goes  on  its 
path  without  deflection.  When  this  is  so  we  know 
that  the  mechanical  forces  on  the  particle  due  to 
electric  and  magnetic  fields  just  balance  each  other. 
That  is 


.         .        .     (b) 
Thus  if  we  apply  to  the  moving  electrified  particle 


14  MOLECULAR   PHYSICS 

simultaneously  an  electric  and  magnetic  field  of  such 
magnitudes  that  the  particle  pursues  its  path  without 
any  deviation,  the  ratio  of  the  strengths  of  the  two 
fields  will  give  us  directly  the  velocity  of  the  particle. 
If,  further,  we  can  measure  the  radius  of  the  circle 
into  which  the  path  of  our  particle  is  bent  by  the 
action  of  the  magnetic  field  alone,  we  can,  by 
equation  (a),  determine  the  value  of  the  ratio 
m/e,  or  the  mass  to  the  charge  for  the  particle  we  are 
investigating,  since  the  value  of  v  is  now  known 
from  the  previous  experiment. 

This  ratio  of  the  mass  to  the  charge  is  one  of  the 
utmost  importance  in  molecular  physics.  It  may 
be  noted  that  for  ions  in  solutions  it  is  the  quantity 
of  matter  associated  with  the  transference  of  unit 
quantity  of  electricity,  that  is  to  say,  the  electro- 
chemical equivalent.  According  to  the  latest  values, 
the  electro-chemical  equivalent  of  hydrogen  ions  in 
solution  is  '0000109  §m-  Per  coulomb.  The  values 
of  the  ratio  for  other  ions  can  be  deduced  from  this 
and  a  table  of  combining  weights  in  the  usual  way, 
since  every  ion  in  solution  carries  by  Faraday's  laws 
either  the  same  charge  as  the  hydrogen  ion  or  some 
simple  multiple  of  it. 

Owing  to  the  way  in  which  the  volt  and  the  ohm 
have  been  defined,  the  former  as  io8  and  the  latter 
as  io9  absolute  electro-magnetic  units,  the  absolute 
unit  of  electro-magnetic  charge  is  ten  times  the 
coulomb  or  practical  unit  of  charge.  The  value  of 
m/e  for  hydrogen  in  absolute  units  of  charge  is, 
therefore,  "000109,  or  Jus^  a  little  greater  than 
io~4  gms.  per  absolute  electro-magnetic  unit  of 
charge.1 

i  The  science  of  electricity  is  burdened  with  two  distinct  systems  of 
units  for  the  measurement  of  electrical  magnitudes,  the  one  founded  on 
the  consideration  of  the  force  with  which  two  similar  charges  repel  each 
other,  the  other  on  considerations  of  the  induction  of  currents  by  mag- 
nets. The  practical  system  of  units  is  founded  upon  the  latter,  the  volt 
being  io8  and  the  ohm  io9  absolute  electro-magnetic  units.  The  ampere 


THE  PHYSICS  OF  THE  ELECTRON     15 

The  principles  just  explained  found  their  first 
application  in  the  experiments  of  Professor  Sir  J.  J. 
Thomson,  on  the  cathode  rays,  experiments  which 
may  well  be  said  to  mark  a  new  era  in  science.  The 
experimental  methods  used  by  him  have  been 


FIG.  2. — CATHODE  RAY  DEFLECTION  TUBE. 

modified  and  improved  upon  in  the  light  of  subse- 
quent discoveries,  and  the  accuracy  attained  in  the 
measurements  greatly  increased.  In  principle,  how- 


and  coulomb  are  thus  i/ioth  of  the  absolute  units  of  current  and  charge. 
To  make  confusion  worse  confounded,  it  has  become  usual  in  works  and 
original  papers  on  these  subjects  to  give  the  value  of  mje  in  electro-mag- 
netic units,  while  the  value  of  e  itself  is  usually  given  in  electrostatic 
units.  Our  statement  that  the  force  on  the  electron  due  to  the  magnetic 
field  is  equal  to  H.e.v  implies  that  we  are  using  the  absolute  electro- 
magnetic system  of  units,  as  this  system  has  been  denned  in  such  a  way 
as  to  make  this  statement  true.  As  this  system  is  the  one  more  closely 
related  to  the  units  in  actual  use,  we  shall  employ  it  throughout,  except 
where  the  contrary  is  explicitly  stated. 


16  MOLECULAR  PHYSICS 

ever,  the  experiments  remain  the  same,  and  on 
account  of  its  historic  interest  the  original  apparatus 
used  in  these  experiments  will  be  described.  Fig.  2 
is  taken  (by  kind  permission  of  Professor  Sir  J.  J. 
Thomson)  from  a  photograph  of  one  of  the  tubes 
used  by  him  for  the  experiment.  The  arrangement 
of  the  various  parts  will  be  seen  more  clearly  from 
the  diagrammatic  representation  in  Fig.  2A. 

The  cathode  of  the  discharge  tube  is  at  C,  and 
consists  of  an  aluminium  disc  supported  by  a  rod 
of  the  same  metal  and  connected  with  the  outside  of 
the  tube  by  a  platinum  wire  sealed  through  the 
glass.  The  anode  R  is  an  aluminium  rod  placed  in 


uii (1 


-I                           ~Lrr± 

D 

J                     1        1  —  r 

~E"~- 

C  A       B 

FIG.  2A. — DIAGRAM  OF  CATHODE  RAY  TUBE. 

a  side  tube,  while  facing  the  cathode  is  a  thick  metal 
disc  A,  filling  the  tube  but  pierced  with  a  small  hole 
through  which  the  cathode  rays  can  pass  in  a  narrow 
pencil.  To  define  this  beam  of  rays  still  further,  a 
second  metal  disc  B  pierced  with  a  still  finer  hole  is 
placed  some  distance  behind  A.  For  convenience 
these  two  discs  are  mounted  in  a  metal  tube  as  shown 
in  the  figure.  This  tube  and  the  anode  R  are  con- 
nected to  earth,  while  R  and  C  are  connected  to  the 
terminals  of  a  large  induction  coil  as  shown  in  the 
photograph. 

Thus,  when  the  discharge  is  passed  between  C 
and  D,  a  very  fine  well-marked  pencil  of  cathode 
rays  emerges  from  B.  It  is  then  made  to  pass 


THE   PHYSICS  OF  THE  ELECTRON     17 

between  two  parallel  plates  D  and  E  of  aluminium 
which  can  be  charged  to  any  required  difference  of 
potential  by  connecting  them  to  a  large  battery  of 
small  accumulators. 

This  part  of  the  tube  is  also  placed  between  the 
poles  of  the  little  electro-magnet  shown  in  the 
photograph,  the  lines  of  magnetic  force  being  at 
right  angles  to  the  plane  of  the  paper  and  therefore 
at  right  angles  to  the  electric  field.  Finally,  the 
stream  of  cathode  particles  falls  upon  the  walls  of 
the  bulb  Z  which  are  covered  with  powdered  zinc 
blende,  its  presence  being  marked  by  a  spot  of  bright 
green  phosphorescent  light  at  the  point  of  impact. 
The  position  of  the  spot  in  the  original  experiments 
was  read  off  on  a  scale  pasted  on  the  outside  of  the 
tube. 

To  perform  the  experiment  the  magnetic  field  is 
first  applied  and  the  deflection  of  the  spot  of  light 
measured.  From  this  deflection  and  the  dimensions 
of  the  different  parts  of  the  tube  it  is  possible  to 
calculate  the  radius  of  the  circle  into  which  the  path 
of  the  rays  has  been  bent  by  the  magnetic  field. 
The  deflected  and  undeflected  paths  of  the  particles 
are  indicated  by  the  dotted  lines  in  the  diagram. 
The  electric  field  is  then  applied  and  the  difference 
of  potential  between  the  two  plates  gradually 
increased  until  the  spot  of  light  is  brought  back  to 
its  original  position.  The  ratio  of  the  electric  to  the 
magnetic  field  is  then  equal  to  the  velocity  of  the 
cathode  particles.  The  value  of  the  ratio  m/e  can 
be  calculated  from  this  velocity  and  the  known 
magnetic  deflection  as  explained  above. 

The  experiments  were  not  without  difficulty.  It 
was  at  first  found  very  difficult  to  obtain  any  deflec- 
tion of  the  particles  by  means  of  an  electric  field. 
This  was  found  to  be  due  to  the  fact  that  the 
passage  of  the  cathode  rays  through  the  residual 
gas  in  the  discharge  tube  rendered  it  more  or  less 
M.P.  3 


i8  MOLECULAR  PHYSICS 

• 

conducting,  so  that  the  particles  were  moving 
through  what  was  practically  a  closed  conductor 
and  were  thus  hardly  affected  by  the  external  electric 
field.  It  was  necessary  in  order  to  eliminate  this 
effect  to  work  with  very  high  vacua. 

On  making  the  calculations  it  was  found  that  the 
velocity  of  the  particles  depended  principally  upon 
the  potential  of  the  discharge,  and  to  some  extent 
also  on  the  pressure  of  the  residual  gas  in  the  tube 
and  the  nature  of  the  electrodes  and  the  gas  in  the 
tube.  Even  in  the  same  tube  the  velocity  of  all  the 
rays  was  not  the  same,  so  that  on  applying  the 
magnetic  field  the  single  spot  of  light  made  by  the 
cathode  beam  on  the  zinc  blende  screen  was  spread 
out  into  a  little  magnetic  spectrum,  as  we  may  call 
it,  each  point  of  which  corresponded  to  cathode  rays 
moving  with  a  definite  velocity.  In  tubes  at  an 
exhaustion  suitable  for  these  experiments  the 
velocities  range,  as  a  rule,  from  2  X  io9  to  3  X  io9 
cms.  per  second,  or  about  i/ioth  of  the  velocity  of 
light. 

On  evaluating  the  ratio  m/e  it  was  not  found  to 
suffer  similar  variations.  The  original  experiments 
showed  and  this  has  since  been  confirmed  by  many 
subsequent  experiments,  that,  whatever  the  nature 
of  the  gas  in  the  discharge  tube,  whatever  the 
material  of  the  cathode,  whatever  the  working 
potential  of  the  tube,  the  value  of  the  ratio  of  the 
mass  of  the  cathode  particle  to  its  charge  is  always 
the  same.  According  to  the  latest  determinations 
the  value  of  this  constant  is  5*65  X  io~8  gms.  per 
unit  of  charge. 

Again,  although  we  have  so  far  considered  only 
the  case  of  the  cathode  rays,  they  are  not  by  any 
means  the  only  source  of  these  corpuscles,  or  elec- 
trons as  they  are  now  called.  Similar  electrons  are 
given  off  in  quantities  from  a  clean  metal  surface 
when  illuminated  by  ultra-violet  light,  or  from  the 


THE   PHYSICS   OF  THE   ELECTRON     19 

surface  of  the  liquid  sodium-potassium  alloy  under 
the  action  of  the  light  from  an  ordinary  candle. 
Rontgen  rays  produce  them  whenever  they  fall  upon 
any  material  object,  and  it  is  interesting  to  note  that 
the  velocity  of  the  electrons  thus  produced  is  the 


FIG.  3. — MAGNETIC  DEFLECTION  OF  THE  CATHODE  RAYS. 

same  as  that  of  the  cathode  rays  in  the  Crookes  tube 
from  which  the  Rontgen  rays  proceed.  Electrons 
are  also  emitted  from  incandescent  metals  at  a  high 
temperature,  and  in  very  large  quantities  when 
certain  metallic  oxides  and  notably  those  of  barium 
and  calcium  are  raised  to  a  red  heat.  These  elec- 

2 — 2 


20  MOLECULAR   PHYSICS 

Irons  have  very  little  velocity  of  their  own,  but  may 
very  readily  be  given  one  by  acting  upon  them  with 
an  electric  field.  If  the  heated  oxide  is  raised  to  a 
potential  P  in  absolute  units,  the  work  done  on  the 
electron  by  the  field  will  be  P  .  e.  liv  is  the  velocity 
acquired  by  the  electron,  its  kinetic  energy  is  ^mv2. 
Hence,  by  the  principle  of  the  conservation  of 
energy  P  .  e  =  %mv2  or  v2  =  2P  .  e/m.  Thus  by 
suitably  altering  the  potential  of  the  hot  oxide  we  can 
give  to  these  electrons  a  suitable  and  known  velocity. 

Fig.  3  is  a  reproduction  of  an  actual  photograph 
of  such  a  discharge.  The  cathode  is  a  platinum  strip 
carrying  a  minute  speck  of  barium  oxide,  raised  to 
a  red  heat  by  means  of  an  electric  current  and 
charged  to  a  potential  of  —  240  volts  from  a  cabinet  of 
small  accumulators.  The  electrons  given  out  by 
the  heated  BaO  are  projected  by  the  field  in  a 
narrow  pencil  and  are  rendered  visible  by  their  action 
on  the  residual  molecules  of  air  in  the  exhausted 
tube.  In  the  photograph  a  magnet  has  been  placed 
behind  the  tube  so  that  there  is  a  magnetic  field  at 
right  angles  to  the  paths  of  the  electrons,  which  are 
thus  bent  into  the  arc  of  a  circle  as  shown  in  the 
figure.  The  fact  that  the  circle  is  not  completed  is 
due  to  the  gradual  diffusion  and  absorption  of  the 
electrons  by  collision  with  the  molecules  of  the  gas 
in  the  tube. 

The  value  of  the  ratio  m/e  for  these  electrons  has 
been  measured  by  their  discoverer  Wehnelt  and 
others.  It  may  be  noticed  that  as  the  potential 
P  to  which  the  cathode  is  raised  is  equal  to  ^v2 .  m/e, 
it  is  only  necessary  to  measure  the  radius  of  the 
circle  into  which  the  rays  are  bent  by  a  magnetic 
field  of  known  strength  H  in  order  to  be  able  to 
calculate  both  v  and  m/e.  This  fact  has  been  applied 
by  Lenard  and  others  to  measure  the  value  of  m/e 
for  the  electrons  given  off  by  metallic  surfaces  under 
the  action  of  ultra-violet  light. 


THE   PHYSICS   OF  THE   ELECTRON     21 
TABLE  I. 


Observer. 

Source  of  electrons. 

ejm  e.m.u.  per  gra. 

Kaufmann 

/3-rays  (slow)  from  Radium 

177    x  io7 

Simon     . 

Cathode  rays 

1-72     x  io7 

Ewers 

£-rays  from  Polonium 

17      x  io7 

Classen  . 

Cathode  rays      .         . 

1774  X  IO7 

t 

Hot  lime     .... 

1-776  X  io7 

Woltz  ;    . 

/3-rays  (slow)  from  Radium 

1767  X  io7 

Bestelmeyer 

Hot  lime     .... 

1766  X  io7 

The  above  table  (Table  I.)  gives  a  few  of  the 
more  recent  determinations  of  the  ratio  e/m  for 
electrons  from  different  sources.  It  will  be  seen 
that  within  very  narrow  limits  indeed,  especially 
considering  the  difficulties  of  the  experiments,  the 
ratio  of  *the  charge  to  the  mass  is  the  same  for  all 
electrons,  whatever  their  origin  and  whatever  their 
velocity,  and  differs  very  little  from  1*77  X  io7. 
The  value  of  m/e  or  the  electro-chemical  equivalent 
of  the  electron,  if  we  may  so  call  it,  is  therefore 
5*65  x  io~8.  For  the  hydrogen  atom,  as  we  have 
seen,  the  value  is  about  io~4.  If  we  could  assume 
that  the  charge  e  is  the  same  for  the  electron  as  for 
the  ion  in  solution  we  see  at  once  that  the  mass  of 
the  electron  must  be  only  about  T^oo  Par^  of  that  of 
the  hydrogen  atom. 

For  this  assumption,  however,  very  little  direct 
evidence  could  be  adduced  at  the  time  it  was  made. 
It  was  one  of  those  strokes  of  genius  which  have 
proved  to  be  correct.  To  determine  absolutely  the 
mass  of  an  electron  we  must  find  some  method  of 
determining  the  value  of  the  electronic  charge  e. 
Fortunately  this  also  has  proved  possible,  owing  to 
a  discovery  made  in  the  Cavendish  laboratory  by 
Mr.  C.  T.  R.  Wilson. 

If    a    space    saturated    with    water    vapour    is 


22  MOLECULAR   PHYSICS 

suddenly  chilled  the  surplus  water  over  and  above 
that  which  would  saturate  the  space  at  the  lower 
temperature  in  general  separates  out  in  little  par- 
ticles of  water,  forming  within  the  space  a  thick  mist 
or  cloud.  It  was,  however,  shown  many  years  ago 
by  Aitken  that  this  condensation  always  commenced 
round  minute  particles  of  dust,  particles  often  far 
too  small  to  be  visible,  yet  sufficiently  material  to  be 
caught  by  a  well-packed  tube  of  cotton  wool.  In 
the  absence  of  these  particles  he  found  that  a  very 
considerable  degree  of  supersaturation  could  be 
produced  without  any  deposition  of  water  and 
without  any  appearance  of  cloud  or  mist,  and  that 
it  was  only  when  the  supersaturation  became  at 
least  eightfold  that  a  mist  or  cloud  was  produced. 
It  appeared  then  that  for  a  lesser  degree  of  super- 
saturation  than  this  the  water  vapour  must  have 
some  nucleus  about  which  to  condense  before  a  drop 
could  be  formed. 

Gases  under  ordinary  conditions  are  almost 
perfect  insulators.  Under  the  action  of  certain 
agents,  such,  for  example,  as  Rontgen  rays  or  any  of 
the  rays  from  radio-active  substances,  a  gas  becomes 
more  or  less  conducting.  It  has  been  shown  that 
this  is  due  to  the  creation  in  the  gas  of  systems, 
some  negatively,  some  positively  charged.  In  all 
probability  these  are  produced  by  the  ionising  agent 
expelling  a  negative  electron  from  the  atom  through 
which  it  passes,  leaving  the  remainder  of  the  mole- 
cule positively  charged.  The  negative  electron 
thus  set  free  soon  attracts  to  itself  one  or  more 
atoms  just  as  an  uncharged  pith  ball  is  attracted  by 
an  electrified  ebonite  rod.  The  gas  thus  becomes 
filled  with  oppositely  electrified  systems  consisting 
of  clusters  of  three  or  four  atoms  together,  which 
move  under  the  action  of  an  electric  field  in  exactly 
the  same  way  as  the  ions  of  an  electrolyte  move  in 
the  electrolysis  of  a  solution.  There  is  this  difference, 


THE   PHYSICS   OF  THE   ELECTRON     23 

however,  that,  whereas  the  electrolytic  ions  are 
stable,  the  gaseous  ions  if  left  to  themselves,  gradually 
re-combine  to  form  neutral  molecules.  Thus  unless 
the  supply  is  kept  up  by  the  continuous  action  of 
the  ionising  agent  the  conductivity  will  soon  die 
away. 

The  mechanism  of  ionisation  by  the  electrons 
emitted  by  a  metal  plate  under  the  action  of  ultra- 
violet light  is  somewhat  different.  Here  the  elec- 
trons have  not  sufficient  energy  to  expel  an  electron 
from  the  atom  and  thus  no  positive  ions  are  produced 
in  the  gas.  The  negative  electrons,  however,  attract 
to  themselves  neutral  molecules  to  form  negative 
ions.  It  will  be  evident  from  the  mode  of  formation 
that  these  ions  bear  the  same  charge  as  the  electron 
which  gave  rise  to  them,  that  is  to  say,  their  ionic 
charge  is  the  same  as  the  electronic  charge  e.  It 
may  be  pointed  out  in  passing  that  since  the  ions  are 
all  of  the  same  sign  and  produced  at  the  same  place, 
namely,  the  surface  of  the  metal  plate,  a  current  can 
only  be  sent  through  the  gas  in  one  direction.  If 
the  metal  plate  is  negative  the  ions  will  be  repelled 
and  thus  carry  a  negative  current  from  it  to  the 
positive  electrode.  If,  however,  the  plate  is  posi- 
tively charged  the  ions  will  be  attracted  back  to  it 
by  the  field  and  the  gas  will  remain  an  insulator. 

It  occurred  to  C.  T.  R.  Wilson  that  these  ions 
might  possibly  serve  as  nuclei  for  the  production 
of  a  fog  or  cloud  in  supersaturated  air,  and  this  was 
found  on  experiment  to  be  the  case.  He  was  able 
to  show  that  drops  of  water  would  condense  on  these 
negative  ions  when  the  supersaturation  was  only 
fourfold,  while  condensation  occurred  on  the  positive 
ions  also  when  the  supersaturation  was  sixfold.  It 
was  found  that  when  the  supersaturation  was 
increased  to  the  proper  extent  each  negative  ion 
became  the  centre  of  a  single  drop  of  water,  and  if 
the  conditions  were  fairly  uniform  these  drops  were 


24  MOLECULAR  PHYSICS 

all  of  the  same  size.  It  will  be  remembered  that  in 
the  case  of  the  ions  formed  by  ultra-violet  light  each 
of  these  drops  will  carry  with  it  the  electronic  charge 
e,  the  magnitude  of  which  we  wish  to  determine. 

Every  drop  in  a  cloud  is  falling  through  the  air 
under  the  action  of  gravity  with  a  definite  velocity. 
Clouds  do  not  float  in  the  air,  though,  if  the  drops 
are  sufficiently  small  they  fall  very  slowly,  owing  to 
the  great  surface  they  present  in  comparison  with 
their  mass  to  the  viscous  drag  of  the  air.  Sir  G.  G. 
Stokes  has  shown  that  if  r  is  the  radius  of  a  small 
drop  of  water  and  q  the  viscosity  of  the  air,  the 
velocity  with  which  the  drop  will  fall  relative  to  the 

2  ft'fi 

air  is  -^— ,  where  g  is,  as  usual,  the  acceleration 

due  to  gravity.  The  drops  formed  round  the  ions 
are  all  of  the  same  size  and  fall  at  the  same  rate. 
We  can  thus  measure  the  velocity  v  of  their  fall  by 
watching  the  rate  at  which  the  surface  of  the  cloud 
settles.  This  will  enable  us  to  calculate  the  radius 
r  of  the  drop,  and  hence  its  mass  M. 

So  far  the  cloud  has  been  falling  freely  under  the 
action  of  gravity.  Let  us  apply  a  field  of  strength  X 
in  such  a  direction  as  to  oppose  the  action  of  gravity, 
that  is  to  say,  with  the  positive  plate  above  the  cloud. 
The  force  on  each  drop  due  to  the  electric  field  is 
then  X  .  e,  while  that  due  to  gravity  is  M  .  g.  We  can 
adjust  the  field  X  until  these  two  forces  exactly 
balance  each  other,  and  the  drop  remains  suspended 
in  air  like  Mahomet's  coffin.  When  this  stage  is 
reached  we  have 

X  .  *  =  M  .  g 

or  e  =  M  .  g/X. 

But  all  these  quantities  are  known,  and  thus  the 
charge  on  the  drop  of  water,  which  we  have  shown  to 
be  the  same  as  that  on  the  original  electron,  can  be 
determined. 

It  remains  to  describe  the  apparatus  devised  for 


THE   PHYSICS  OF  THE  ELECTRON     25 


the  experiment.  It  is  shown  in  Fig.  4.  It  is  well 
known  that  if  a  mass  of  gas  is  expanded  in  such 
a  way  that  no  heat  is  allowed  to  enter  or  leave  it, 
the  temperature  will  fall.  The  lowest  temperature 
reached  in  any  given  expansion  can  be  calculated 


t 


R 


t 


FIG.  4. — C.  T.  R.  WILSON'S  EXPANSION  APPARATUS. 

from  the  gas  laws  if  the  ratio  of  the  specific  heats  of 
the  gas  is  known.  As  gases  are  bad  conductors  of 
heat  we  can  satisfy  the  conditions  of  the  experiment 
by  making  the  expansion  sufficiently  rapid.  The 
mass  of  the  gas  is  then  cooled  down  to  the  calculated 


26  MOLECULAR   PHYSICS 

temperature  before  any  appreciable  amount  of  heat 
has  had  time  to  enter  the  system. 

The  method  of  making  the  expansion  will  be 
clear  from  the  diagram.  The  tube  H  connects 
with  a  large  bulb  of  some  litres  capacity  kept 
exhausted  by  means  of  a  water  pump.  It  is  closed 
by  a  rubber  stopper  C  which  can  be  suddenly  with- 
drawn by  means  of  the  rod  R,  thus  creating  practi- 
cally instantaneously  a  partial  vacuum  in  this  part 
of  the  apparatus.  The  air  being  thus  suddenly 
withdrawn  from  beneath  it,  the  light  glass  plunger  P 
which  had  been  adjusted  to  a  suitable  height  in 
the  cylinder  D  is  forced  down  with  great  rapidity, 
thus  producing  within  the  experimental  chamber  L 
a  very  rapid  expansion  of  an  amount  which  depends 
only  upon  the  initial  position  of  the  plunger  P.  The 
temperature  in  L  is  therefore  suddenly  lowered  to  a 
degree  which  can  be  calculated,  and  if  the  air  in  L 
was  previously  saturated  it  will  now  be  super- 
saturated to  an  extent  which  is  measured  by  P/p 
where  P  and  p  are  the  vapour  pressures  of  water  at 
the  initial  and  final  temperatures. 

In  making  an  experiment  the  air  in  L  is  freed 
from  all  material  nuclei  by  repeated  expansions ; 
the  plunger  is  adjusted  so  as  to  make  the  super- 
saturation  after  expansion  rather  more  than  fourfold, 
the  upper  plate  E,  which  is  usually  of  zinc,  is  illu- 
minated with  ultra-violet  light  for  a  moment  in 
order  to  produce  a  suitable  supply  of  negative  ions 
in  the  gas  and  the  expansion  is  made.  A  cloud  is 
formed  on  the  negative  ions  and  the  rate  at  which 
the  surface  of  it  settles  is  taken.  After  it  has  fallen 
some  little  distance  the  upper  plate  E,  which  had 
been  previously  uncharged,  is  raised  to  a  positive 
potential,  and  its  potential  adjusted  until  the  surface 
of  the  cloud  is  seen  to  remain  stationary.  If  V  is 
this  potential  and  the  lower  plate  at  a  distance  d  from 
the  upper  one  is  earthed,  the  strength  of  the  electric 


THE   PHYSICS   OF  THE   ELECTRON     27 


field  is  V/d  and  the  electronic  charge  e  is  equal  to 
Mgrf/V,  where  M  has  been  calculated  by  Stokes' 
law  from  the  rate  of  fall  of  the  cloud. 

The  method  was  first  applied  in  a  rather  different 
form  by  Professor  Sir  J.  J.  Thomson.  In  the  form 
described,  which  is  the  one  which  has  been  used  with 
the  greatest  success,  it  was  performed  by  H.  A. 
Wilson.  We  have,  for  the  sake  of  making  our 
argument  logically  complete,  considered  the  case  of 
the  electrons  produced  by  ultra-violet  light,  for  in 
this  case  we  have  evidence  that  the  charge  we  are 
measuring  is  really  that  carried  by  an  electron.  It  has 
been  shown,  however,  experimentally,  that  the  value 
of  the  charge  e  is  the  same  no  matter  how  the  ions 
are  produced.  Experiments  carried  out  with  ions 
produced  by  Rontgen  rays  or  the  various  rays  from 
radio-active  materials  gave  exactly  the  same  values 
for  the  charge  e.  Like  the  ratio  m/e,  the  charge  e  is 
a  universal  constant.  Some  recent  determinations 
of  it  are  given  in  the  following  table. 

TABLE  II. 


Roux 


Planck . 


server. 

Carrier. 

t  (electrostatic 
units). 

nan 

ihaft     . 
an 

Water  drops  (original  method) 
Sulphur  drops 
Metallic  dust  .... 
Oil  or  mercury  spray 

4-67  X  io-10 
4-17  X  io-10 
4*65  X  io-10 
4-89  X  io-10 

;rford   . 
k. 

[Counting  the  a-rays] 
Theory  of  radiation 

4-65  X  io-10 
4-69  X  io-10 

It  will  be  seen  from  Table  II.  that  the  values 
obtained  for  the  electron  charge  e  by  different 
observers  working  in  different  ways,  though  not  so 
consistent  as  those  obtained  for  the  ratio  e/m,  yet 


28  MOLECULAR  PHYSICS 

do  not  differ  much  from  a  mean  value  of  about 
47  X  10  ~ 10  electrostatic  units,  or  1-57  X  io~20in 
the  absolute  electromagnetic  unit  of  charge  which 
is  equal  to  10  coulombs. 

The  most  extensive  survey  of  the  subject  has 
been  made  by  Millikan  (see  Physical  Review,  1911). 
Instead  of  water  drops  he  used  very  fine  globules 
of  oil  or  sometimes  mercury  produced  by  an  atomiser 
or  fine  spray.  These  drops  could  be  passed  as 
required  into  his  apparatus,  which  very  much 
resembled  the  chamber  L  in  Fig.  4,  through  a  small 
hole  made  in  the  top  plate.  These  globules  did  not 
evaporate  appreciably,  so  that  an  individual  drop 
could  be  isolated  and  kept  under  observation 
through  a  microscope  for  several  hours  consecu- 
tively. The  microscope  was  fitted  with  an  engraved 
glass  scale  in  the  eyepiece,  on  which  the  whole 
of  the  measurements  on  the  motion  of  the  drop 
could  be  made  very  accurately  and  conveniently. 
By  properly  adjusting  the  difference  of  potential 
between  the  upper  and  lower  plates  the  drop  could 
be  kept  in  the  field  of  view  during  the  whole  of  the 
experiment.  The  measurements  made  and  the 
calculation  of  the  charge  are  precisely  the  same  for 
the  oil  globule  as  for  the  water  drop. 

These  drops  were  not  originally  charged,  but 
picked  up  their  charges  from  the  surrounding  air, 
which  was  ionised  either  by  Rontgen  rays  or  by 
radium.  These  comparatively  large  globules  could 
collect  and  carry  more  than  one  electronic  charge, 
seven  or  eight  being  a  very  usual  number,  though 
some  drops  had  many  more  than  this.  The  inter- 
change of  charges  between  the  globule  and  the  air 
could  be  easily  observed  with  the  microscope.  The 
drop  which  had  been  poised  almost  motionless  in  the 
air  for  some  time  by  the  balanced  action  of  gravity 
and  the  electric  field  would  be  seen  to  dart  suddenly 
upwards,  showing  that  the  drop  had  captured 


THE  PHYSICS  OF  THE  ELECTRON     29 

another  charge  and  thus  caused  the  electric  force  to 
increase,  or  perhaps  on  the  other  hand  the  drop 
would  be  seen  to  fall,  having  parted  with  one  of  its 
charges  to  some  colliding  molecule. 

The  important  point  brought  out  by  the  experi- 
ment is  that  in  every  case  it  was  found  that  the 
magnitude  of  the  charge  thus  exchanged,  which 
could  be  calculated  by  a  simple  application  of  the 
principles  already  explained,  was  exactly  the 
electronic  charge  e,  and  the  total  charge  on  the 
globule  at  any  time  was  always  very  exactly  some 
integral  multiple  of  this  charge.  An  examination 
of  the  mass  of  figures  collected  by  Professor  Millikan 
leaves  no  room  for  doubting  that  the  charge  which 
we  have  denoted  by  e  is  a  universal  constant,  and 
that  every  electrical  charge  is  made  up  of  an 
integral  number  of  electrons,  just  as  every  fragment 
of  an  element  is  made  up  of  a  whole  number  of 
atoms. 

From  Table  I.  we  have  the  ratio  e/m,  equal  to 
177  X  io7,  -  for  all  electrons.  Combining  this 
result  with  the  value  just  obtained  for  e  we  are 
driven  to  the  conclusion  that  whatever  the  source 
from  which  they  come  all  electrons  have  identically 
the  same  mass  and  charge,  the  former  being  8 '8  X 
io~28gms.,  the  latter  1*57  X  io~19  coulombs.  Such 
particles  must  form  a  constituent  part  of  all  matter. 

The  value  of  e  ascribed  to  Professor  Rutherford 
and  also  included  in  Table  II.  was  obtained  irom 
experiments  of  an  entirely  different  nature  made  on 
the  a-particles.  Before  passing  to  these  we  must 
refer  very  briefly  to  an  exceedingly  beautiful 
extension  of  the  method  of  drops  which  has  recently 
been  brought  to  perfection  by  the  originator  of  the 
experiments. 

In  the  experiments  already  described,  the  clouds 
obtained  were  fairly  uniform,  as  the  ionisation  was 
intense  and  time  was  given  for  the  ions  formed  to 


30  MOLECULAR   PHYSICS 

diffuse  through  the  body  of  the  gas.  Suppose,  how- 
ever, that  we  allow,  say,  a  single  a-particle  to  cross 
our  expansion  chamber  and  at  the  same  time  make 
an  expansion  of  the  air  in  the  chamber  by  the  method 


FIG.  5. — THE  TRACKS  OF  THE 

already  described.  The  particle  passes  through  the 
air,  ionising  it  as  it  passes,  and  thus  leaving  behind  it 
a  trail  of  charged  ions.  Water  drops  at  once  form 
upon  these  from  the  now  supersaturated  air  before 
they  have  had  time  either  to  diffuse  into  the  rest  of 


THE   PHYSICS   OF  THE   ELECTRON     31 


the  gas  or  to  recombine.  If  the  expansion  chamber 
is  suitably  illuminated  these  drops  appear  as 
brilliant  points  of  light  all 
along  the  path  traversed 
by  the  particle.  In  the 
case  of  the  a-particle  the 
ions  are  so  numerous  that 
the  track  of  the  particle 
becomes  visible  as  a  con- 
tinuous shining  streak  of 
light.  In  the  case  of  an 
electron  where  the  ioriisa- 
tion  is  less  intense  the  ap- 
pearance presented  is  that 
of  a  string  of  bright  beads. 
We  are  thus  able  not 
merely  to  detect,  but  even 
to  follow  the  path  of  a 
single  particle  of  any  kind 
providing  it  produces  ioni- 
sation  in  a  gas. 

By  the  kindness  of 
Mr.  C.  T.  R.  Wilson,  I 
am  able  to  reproduce  'two 
of  the  photographs  taken 
by  him  in  this  way.  In 
Fig.  5  are  shown  the  paths 
of  a  number  of  a-particles. 
These  have  their  origin  in 
a  small  sample  of  radium 
placed  just  outside  the 
chamber  and  shoot  across 
the  chamber  as  shown  in 
the  photograph  until  finally 

their  energy,  which  is  being  spent  in  the  work  of 
separating  the  ionic  charges  along  the  whole  of  the 
path,  finally  becomes  too  small  to  produce  ionisation, 
and  the  particles  disappear  from  human  ken. 


A 

FIG.  6. — RONTGEN  RAYS. 


32  MOLECULAR  PHYSICS 

Fig.  6  is  a  photograph  of  the  passage  of  a 
narrow  beam  of  Rontgen  rays  through  the  expansion 
chamber,  from  A.  to  A/  We  have  mentioned  before 
that  the  Rontgen  rays  produce  rapidly-moving 
cathode  rays  when  they  fall  upon  matter ;  in  this 
remarkable  photograph  these  cathode  rays  are 
made  visible  to  us  by  the  ions  they  produce.  Here 
upon  the  dark  background  their  tracks  may  be  seen 
as  a  tangled  skein  of  bright  threads  radiating  out 
from  the  invisible  track  of  the  Rontgen  rays.  Each 
single  thread  represents  the  whole  path  of  a  single 
electron  from  its  expulsion  from  the  parent  molecule 
under  the  action  of  the  Rontgen  rays,  to  the  place 
where  it  finally  becomes  too  weak  to  ionise.  In  some 
of  the  brighter  threads  the  individual  drops  are 
clearly  to  be  seen.  The  twists  and  turns  in  each 
little  path  are  due  to  collisions  between  the  cathode 
particle  and  the  molecules  of  the  surrounding  air, 
or,  rather,  perhaps,  with  the  individual  electrons 
contained  in  these  molecules. 

These  photographs  will  perhaps  do  more  than 
any  argument,  however  cogent,  to  remove  any  doubt 
which  may  still  be  felt  as  to  the  objective  reality 
of  the  electrons  and  other  particles  with  which  we 
have  been  dealing.  Nothing  but  an  actual  particle 
could  leave  behind  it  such  tracks  as  those  shown  in 
the  photographs  we  have  reproduced. 

We  have  not  space  to  deal  with  the  many 
difficulties  of  the  experiment  or  with  the  skill  and 
ingenuity  with  which  they  have  been  overcome. 
Those  interested  may  be  referred  to  the  original 
paper  in  the  Proceedings  of  the  Royal  Society  for  1912. 

The  method  is  still  in  its  infancy,  and  the  photo- 
graphs so  far  obtained  are  hardly  more  than  trial 
exposures.  Already,  however,  several  heated  con- 
troversies have  been  settled,  and  many  cherished 
hypotheses  dethroned,  as  the  result  of  the  photo- 
graphs obtained.  To  those  of  us  who  have  been 


THE  PHYSICS  OF  THE  ELECTRON     33 

working  by  indirect  methods  on  some  of  the  more 
obscure  problems  still  left  to  us  for  solution,  the 
method  has  come  as  a  veritable  giving  of  sight  to 
the  blind,  and  now  that  Mr.  C.  T.  R.  Wilson  has 
perfected  his  apparatus  and  can  turn  his  attention 
to  using  it  as  an  instrument  of  research  we  may  hope 
for  many  interesting  and  important  results  in  the 
near  future. 


M.p. 


CHAPTER    III. 
THE  POSITIVE  PARTICLE. 

WE  have  already  seen  that  positively  charged 
particles  are  projected  with  high  velocities  from 
radium  and  other  radioactive  substances,  and  that 
they  are  also  to  be  found  in  discharge  tubes.  Unlike 
the  electron  the  positive  particle  has  a  mass  com- 
parable with  that  of  an  atom,  no  positive  charge 
having  yet  been  detected  in  association  with  any 
mass  less  than  that  of  an  hydrogen  atom.  The 
charge  on  a  positive  particle  is,  however,  either  the 
same  as  that  on  an  electron  or  some  simple  multiple 
of  it.  The  a-rays,  as  the  particles  from  radioactive 
substances  are  still  called  (a  relic  of  the  time  when 
their  nature  was  unknown)  always  carry  a  charge 
of  2  .  e.  In  discharge  tubes,  however,  positive 
particles  are  found  with  all  integral  multiples  up  to 
8  .  e.  We  shall  see  that  we  may  regard  the 
positive  particles  as  atoms  travelling  with  a  high 
speed  from  which  one  or  more  electrons  have  been 
removed. 

The  positive  particle  can  be  deflected  by  electric 
and  magnetic  fields  in  the  same  way  as  the  negative 
electron,  and  obeys  the  same  laws.  The  deflection 
is  in  each  case  in  the  opposite  direction  to  that  of 
the  electron,  while,  owing  to  the  greater  mass,  the 
deflection  is  less  than  that  for  a  similarly  moving 
electron.  The  great  ionising  power  of  the  positive 
particles  makes  the  detection  of  the  electrical 
deflection  difficult.  For  these  and  other  experi- 
mental reasons  it  is  only  recently  that  much  light 


THE   POSITIVE  PARTICLE  35 

has  been  thrown  on  their  nature  and  properties. 
These  difficulties  have  now  been  overcome,  and 
the  positive  particle  also  is  beginning  to  yield  up 
its  secrets.  As  the  positive  particle  is  always  an 
atom  of  some  kind,  its  investigation  is,  perhaps, 
from  some  points  of  view  of  even  greater  interest 
than  that  of  the  electron. 

The  greater  energy  of  these  particles  is,  however, 
in  some  ways  an  advantage.  It  enables  us  to  deal 
with  individual  particles,  whereas  in  the  case  of 
the  electron  we  can  only  deal  with  large  numbers. 
Thus  our  measurements  gain,  perhaps,  in  definiteness 
although  they  may  lose  somewhat  in  numerical 
precision. 

If  e  be  the  charge  on  a  single  a-particle,  the  total 
charge  carried  by  N  particles  is  N  .  e,  and  if  N  is 
sufficiently  large  this  charge  will  be  large  enough  to 
be  directly  measured  by  an  electroscope  or  electro- 
meter. If  we  can  further  determine  the  number  of 
particles  carrying  this  charge  we  shall  have  made  a 
direct  determination  of  the  charge  e. 

The  experiments  are  best  performed  using  the 
a-particles  from  radium,  polonium,  or  some  other 
radioactive  substance.  They  were  carried  out 
almost  simultaneously  by  Rutherford,  and  by 
Regener.  In  Rutherford's  experiments  the  a-par- 
ticle was  detected  by  the  ionisation  it  produced  in  a 
special  chamber  ;  the  entry  of  each  a-particle  into 
the  apparatus  -being  notified  by  a  kick  of  the  needle 
of  a  sensitive  electrometer.  In  Regener's  experi- 
ments the  number  of  scintillations  produced  by  the 
particles  in  a  given  time  on  a  fluorescent  screen  was 
counted.  The  former  method  was  the  more  satis- 
factory from  a  theoretical  view,  as  there  was  at  the 
time  no  direct  evidence  that  every  particle  produced 
a  scintillation  when  it  struck  a  screen,  although  this 
has  since  been  shown  to  be  the  case  by  Rutherford. 
It  was  also  proved  by  the  fact  that  the  two  experi- 

3—2 


36  MOLECULAR  PHYSICS 

menters  reached  almost  exactly  the  same  value  for 
the  charge  on  the  a-particle.  The  experiment  of 
Regener  is  simpler  to  carry  out  than  the  electrical 
method  of  Rutherford,  and  granting  his  assumptions, 
is  probably  capable  of  greater  accuracy. 

Regener's  apparatus  is  shown  in  Fig.  7.     Fig.  7a 
shows    the    "  counting "    apparatus,   Fig.    7b   the 


FIG.  7. — REGENER'S  APPARATUS. 

apparatus  for  measuring  the  total  charge  carried  by 
the  rays. 

The  counting  apparatus  is  very  simple.  It 
consists  of  a  long  tube  closed  at  one  end  by  a  brass 
plate  c,  c,  bored  with  a  circular  hole  some  centimetre 
in  diameter.  Across  this  is  sealed  a  thin  glass  cover- 
slip  bearing  on  its  under  surface  the  fluorescent 
screen  D,  in  this  case  a  thin  plate  cut  from  a  crystal 
of  brown  diamond,  a  substance  chosen  by  Regener 
after  many  trials  as  the  most  suitable  for  the 


THE   POSITIVE  PARTICLE  37 

purpose.  Rutherford  has  since  used  prepared 
screens  of  powdered  willemite  with  equal  success. 

A  high  power  microscope  was  focussed  on  the 
diamond  plate  for  viewing  the  scintillations  which, 
numbering  about  one  every  two  seconds,  were 
easily  counted.  The  source  of  the  a-particles  in 
Regener's  experiments  was  a  plate  of  polonium, 
placed  at  P,  some  127  cms.  from  the  diamond  screen. 
The  whole  tube  was  carefully  exhausted  so  that  there 
should  be  no  absorption  of  the  particles  before 
reaching  the  screen. 

The  number  of  scintillations  in  a  given  time  was 
counted,  and  the  area  A  of  the  aperture  in  the  brass 
plate  and  its  distance  R  from  the  polonium  carefully 
determined.  If  n  is  the  number  of  particles  hitting 
the  screen  in  a  time  t  seconds,  then  the  number  of 
particles  emitted  by  the  polonium  per  second  across 
a  hemisphere  drawn  about  its  upper  surface  is 

27iR2  n 

N  =  ^--p 

assuming  that  the  particles  are  given  out  equally  in 
all  directions.  This  assumption  was  verified  by 
Rutherford  in  a  separate  experiment.  For  the  disc 
used  by  Regener  N  was  found  to  be  3*935  X  io5. 

To  measure  the  total  charge  carried  by  the 
a-particles  from  the  disc  a  Faraday  cylinder  was 
used.  This  consisted  of  a  partially  closed  brass 
cylinder  F  (Fig.  7b)  enclosed  in  a  glass  chamber 
exhausted  to  a  very  high  vacuum  to  avoid  any  loss 
of  charge  by  ionisation  in  residual  air.  The  polo- 
nium was  mounted  at  P  so  that  the  a-particles  from 
its  upper  surface  entered  the  cylinder.  Here  they 
gave  up  their  charges  to  it,  gradually  raising  it  to  a 
positive  potential,  which  could  be  measured  by  an 
electrometer  or  electroscope  connected  to  the  metal 
electrode  E. 

This  method  of  measuring  small  currents  by  the 
electrometer  is  one  in  e very-day  use  in  this  class  .of 


38  MOLECULAR   PHYSICS 

experimental  work  and  deserves  a  little  further  con- 
sideration. Let  C  be  the  electrical  capacity  of  the 
Faraday  cylinder  and  its  connections,  and  suppose 
the  cylinder  is  placed  at  zero  potential  by  connecting 
it  to  earth.  Insulate  and  note  the  reading  after 
some  suitable  interval  of  time,  say  t  seconds.  .Let 
V  be  the  potential  corresponding  to  this  reading  ; 
this  can  easily  be  determined  by  calibrating  the 
instrument  with  suitable  known  potentials.  The 
charge  given  to  the  electrode  in  the  time  t  is  then 
CV.  so  that  the  current  between  P  and  F  is  CV/t. 

Since  the  capacity  of  a  system  can  be  made  very 
small  the  method  is  far  more  sensitive  than  the  most 
delicate  galvanometer.  The  capacity  of  an  electro- 
scope of  the  C.  T.  R.  Wilson  type  with  its  electrode 
and  all  its  connections  need  not  be  greater  than  4  or 
5  cms. ;  or,  say,  5  X  10  - 12  farads.  The  electroscope 
will  easily  give  a  deflection  of  100  divisions  for  a 
potential  of  I  volt,  while  a  movement  of  the  gold 
leaf  of  a  division  per  minute  can  be  detected  with 
certainty.  This  corresponds  to  a  current  of  10  - 15 
amperes.  The  best  galvanometers  give  a  perceptible 
deflection  for  a  current  of  about  io-n  amperes. 
The  electroscope  method  is,  therefore,  about  ten 
thousand  times  as  sensitive  as  the  most  delicate 
galvanometer. 

In  the  present  case  the  value  of  C.V.//  gives  the 
charge  carried  by  the  a-particles  per  second  from  the 
upper  surface  of  the  polonium  disc.  In  electro- 
static units  it  was  found  to  be  -000377.  This  was 
the  charge  carried  by  the  3*935  X  io5  a-particles 
emitted  by  the  polonium.  The  charge  on  each 
particle  was  therefore  "000377/3 -935  X  io5  or 
9-58  X  io  -10  in  electrostatic  units.  Rutherford's 
value  was  9*30  X  io  ~ 10  in  the  same  units. 

It  will  be  seen  that  these  numbers  are  almost 
exactly  twice  the  value  47  X  io~10  e.s.u.,  which 
represents  the  mean  value  for  the  electronic  charge  e. 


THE   POSITIVE    PARTICLE  39 

In  fact  the  value  of  2  .  e  is  almost  midway  between 
these  experimental  numbers.  The  charge  on  the 
a-particle  is  therefore  exactly  twice  the  charge  on 
the  electron.  The  a-particle  is  therefore  an  atom 
which  has  lost  two  electrons.  This  is  characteristic 
of  all  the  a-particles  emitted  by  radioactive 
substances  which  appear  to  differ  from  each  other 
only  in  velocity. 

We  have  stated  that  the  a-particle  is  an  atom  ; 
the  question  arises  of  what  element  is  it  an  atom  ? 
The  ratio  of  the  mass  to  the  charge  can  be  determined 
for  the  a-particle  in  the  same  way  as  for  the  electron, 
neglecting  the  different  experimental  arrangements 
required.  No  great  accuracy  has,  however,  been 
reached,  as  Ihe  deflection  of  these  particles  from 
radioactive  substances  even  in  the  strongest  magnetic 
fields  is  small.  According  to  Rutherford,  the  ratio 
of  mass  to  charge  for  the  a-particle  from  radium  is 
1*97  x  io~4,  and  we  have  seen  that  they  carry  two 
charges,  or  in  the  language  of  electrolysis,  are  di- 
valent. The  electrochemical  equivalent  of  hydrogen 
is  io~4,  so  that  if  we  can  assume  that  the  ion  in 
solution  carries  the  electronic  charge  e,  the  atomic 
weight  of  the  a-particles  would  be  3*84,  which  is 
very  near  3*96,  the  atomic  weight  of  helium.  Con- 
versely, if  we  can  show  that  the  a-particle  is  an  atom 
of  helium  we  shall  have  direct  evidence  that  our 
assumption  that  the  monovalent  ion  carries  the 
same  charge  as  an  electron  is  correct. 

The  proof  of  the  nature  of  the  a-particle  has  been 
given  by  Rutherford  to  whom  we  owe  so  much  of 
our  knowledge  of  these  rays.  The  experiment  is 
based  on  the  fact  that  the  a-rays,  owing  to  the  great 
speed  with  which  they  are  projected  by  the  parent 
molecule,  are  able  to  pass  through  thin  sheets  of 
solid  substances  which  are  perfectly  impervious  to 
the  molecules  of  ordinary  gases. 

The  substance  used  as  the  source  of  a-particles 


40  MOLECULAR  PHYSICS 

was  radium  emanation,  the  radioactive  gas  which  is 
the  first  decomposition  product  of  radium,  and  on 
which  Professor  Ramsay  proposes  to  bestow  the 
name  of  niton.  This  gas,  which  is  disengaged  from 
solutions  of  radium  in  water,  after  being  purified  in 
various  ways,  is  finally  passed  into  a  fine  thin- walled 
glass  tube,  the  end  of  which  has  been  carefully 
sealed.  This  is  enclosed  by  a  wider  thick-walled 
glass  tube  which  is  also  made  quite  air-tight  and  has 
in  its  upper  portion  two  electrodes.  The  spectrum 
of  the  discharge  between  these  two  electrodes 
enables  us  to  determine  the  nature  of  the  gases  in 
this  outer  tube.  There  is  no  connection  between  the 
inner  and  outer  tubes,  so  that  nothing  can  pass  from 
the  one  to  the  other,  except  the  a-rays.  This  point 
was  tested  by  filling  the  inner  tube  with  helium  and 
allowing  the  apparatus  to  stand  for  some  days.  No 
trace  of  the  helium  spectrum  was  obtained  in  the 
outer  tube  under  these  circumstances.  When,  how- 
ever, the  inner  tube  was  filled  with  emanation,  the 
a-particles  emitted  were  able  to  pass  through  the 
thin  glass  walls  and,  being  stopped  by  the  thicker 
tube  beyond,  collected  in  the  space  between  the  two 
tubes. 

Slowly,  as  the  experiment  went  on,  the  spectrum 
of  helium  began  to  appear,  becoming  brighter  and 
more  complete  as  more  and  more  of  the  rays  passed 
through  the  inner  tube,  until  at  the  end  of  a  few 
hours  the  complete  helium  spectrum  was  obtained. 
The  blank  experiments  were  far  more  in  number  and 
severity  than  has  been  described  here.  They  left 
no  doubt  that  the  a-particles  were  indeed  atoms  of 
helium,  differing  from  the  ordinary  atoms  of  the  gas 
only  in  their  velocity  and  charge.  We  have  seen 
above  that  this  result  leads  directly  to  the  conclusion 
that  the  charge  on  a  monovalent  ion  in  solution  is 
the  atom  of  electricity  which  we  denote  by  e. 

This  is  one  of  the  most  direct  proofs  of  this  very 


THE  POSITIVE  PARTICLE  41 

important  fact.  There  are,  however,  many  others 
of  very  diverse  natures,  some  of  which  we  shall 
have  occasion  to  discuss  when  dealing  with  the 
phenomena  on  which  they  are  founded. 

The  charge  carried  by  a  monovalent  ion  in 
solution  and  the  electronic  charge  are  thus  the  same; 
the  value  for  the  latter  is,  as  we  have  seen,  very 
near  47  X  io~10£.s.^.,  or  1*57  x  io~20  in  our  electro- 
magnetic units.  The  ratio  of  the  mass  to  the 
charge  for  the  hydrogen  atom  is,  as  we  have  seen, 
1-04  X  io~  4.  Thus  the  mass  of  the  hydrogen  atom 
is  1*04  X  10  ~ 4  e,  or  1-63  x  io~24gms.  This  is  there- 
fore the  value  in  grammes  of  the  chemical  unit  of 
atomic  weight,  and  we  can  at  once  calculate  from  it 
the  actual  mass  of  any  atom  of  which  the  chemical 
atomic  weight  is  known.  The  accuracy  of  the 
result  depends  only  on  the  accuracy  with  which  the 
value  of  e  can  be  determined.  A  reference  to 
Table  II.  (see  page  27)  will  show  that  the  error  in 
the  value  we  have  used  probably  does  not  exceed 
2%,  or  3%  at  most. 

Since  the  mass  of  a  cubic  centimetre  of  hydrogen 
at  normal  temperature  and  pressure  is  almost 
exactly  9  x  io~5  gms.,  the  number  of  hydrogen 
molecules  contained  in  I  cub.  cm.  of  a  gas  under 
these  conditions  is  9  X  io~5/2  X  1*58  X  io~24,  or 
275  X  iovl9.  By  Avogadro's  hypothesis  this 
number  is  independent  of  the  nature  of  the  gas. 


CHAPTER   IV. 

THE  NEW  METHOD  OF  ANALYSIS. 

WE  have  considered  so  far  the  case  of  the 
positively  charged  particles  from  radioactive  sub- 
stances, and  have  seen  how  their  mass,  charge,  and 
chemical  nature  have  been  determined,  and  how 
these  determinations  have  given  us  the  most  certain 
and  accurate  estimate  of  the  actual  mass  of  a  hydrogen 
atom.  The  information  obtainable  was,  however, 
limited  by  the  fact  that  these  particles  are  all  of  one 
kind,  consisting  always  of  atoms  of  helium. 

We  have  already  mentioned  that  it  is  possible, 
in  a  discharge  tube,  to  endow  atoms  and  molecules 
of  ordinary  matter  with  those  properties  of  high 
velocity  and  electric  charge  which  have  made  the 
a-particles  so  amenable  to  experiment.  The  pro- 
cess may  be  regarded  as  follows.  When  the  two 
electrodes  of  the  discharge  tube  are  connected  to 
the  poles  of  an  induction  coil,  the  molecules  of  the 
rarefied  gas  in  the  tube  are  subjected  to  a  very 
strong  electric  tension.  This  tension  acting  upon 
the  negative  electrons,  which,  as  we  have  seen,  are 
contained  in  all  molecules,  causes  one  or  more  of 
them  to  be  displaced  from  the  molecule,  leaving  the 
remainder  positively  charged.  This  positive  particle, 
as  we  may  now  call  it,  is  driven  with  great  velocity 
towards  the  cathode  by  the  action  of  the  electric 
field  which  produced  it. 

If  the  cathode  is  suitably  perforated,  the  positive 
particle  will  pass  through  it,  and  emerge  on  the 


THE  NEW  METHOD  OF  ANALYSIS  43 

further  side  with  this  velocity  unimpaired.  It  can 
then  be  detected  by  allowing  it  to  fall  either  on  a 
fluorescent  screen,  or  preferably  on  a  photographic 
plate,  where  it  will  produce  a  permanent  record, 
which  can  be  measured  at  leisure  with  suitable 
instruments  of  precision. 

The  experiments,  for  reasons  to  which  we  have 
already    alluded,    presented   many   difficulties.     It 


FIG.  8. — THOMSON'S  POSITIVE  RAY  APPARATUS. 

is  only  after  several  years  of  experiment  that 
Professor  Sir  J.  J.  Thomson  has  at  last  perfected 
an  apparatus  which  allows  him  to  measure  these 
particles  with  accuracy  and  certainty. 

A  general  idea  of  the  apparatus  can  be  obtained 
from  Fig.  8,  which  is  reproduced  from  a  photograph 
of  one  of  Professor  Thomson's  tubes.  The  details 
are  shown  more  clearly  in  the  accompanying 


44  MOLECULAR  PHYSICS 

diagram,  Fig.  9,  which  represents  a  section  of  part 
of  the  apparatus  as  seen  from  above. 

The  apparatus  consists  of  two  parts  :  the  dis- 
charge tube  proper,  where  the  particles  are  produced 
and  the  "  camera/'  where  their  presence  is  detected 
and  their  masses  determined.  The  discharge  tube 
proper  consists  of  a  large  bulb  T,  some  30  cms.  in 
diameter.  The  anode  A  (Fig.  8)  is  placed  in  a  side  tube, 
while  the  cathode  C  (Fig.  9)  occupies  the  neck  of  the 
bulb.  The  gas  to  be  experimented  on  enters  the 


FIG.    9.— THOMSON'S  POSITIVE  RAY  TUBE. 

bulb  through  the  tubes  at  e,  and  is  removed  through 
the  tube  g  by  a  Gaede  pump,  which  is  worked 
sufficiently  rapidly  to  keep  the  gas  in  T  at  a  suitably 
low  pressure. 

The  cathode  C  (Fig.  9)  is  an  aluminium  rod 
pierced  with  a  very  fine  copper  tube  about  8  cms. 
long  and  less  than  i-ioth  mm.  in  diameter.  An 
exceedingly  fine  pencil  of  positive  rays  is  thus 
obtained.  It  is  evident  that  with  a  tube  so  narrow 
any  stray  magnetic  field  will  cause  the  particles  to 
hit  the  walls  of  the  tube  and  be  lost.  To  prevent 


THE  NEW  METHOD  OF  ANALYSIS  45 

this  the  copper  tube  is  enclosed  for  the  greater  part 
of  its  length  in  a  thick  iron  tube  S,  shaded  in  the 
diagram,  while  thick  iron  screens  I,  I,  protect  the 
main  discharge  from  the  influence  of  the  magnet. 

Owing  to  the  intensity  of  the  discharge,  the 
cathode  becomes  very  hot,  and  it  is  necessary,  in 
order  to  protect  the  numerous  sealing  wax  joints, 
to  surround  them  with  a  water  cooling  jacket,  as 
shown  in  Fig.  8. 

On  leaving  the  copper  tube,  the  rays  pass  between 
M  and  N,  two  soft  iron  blocks  let  in  through  the  sides 
of  the  tube  (which  is  here  made  of  ebonite)  and 
carefully  waxed  round,  so  as  to  be  completely 
vacuum  tight.  These  blocks  serve  two  purposes. 
In  the  first  place,  they  form  the  pole  pieces  of  the 
electromagnet  E,  E,  from  which,  however,  they  are 
electrically  insulated  by  two  thin  strips  of  mica  m,  m. 
This  insulation  enables  them  to  be  charged  positively 
and  negatively  respectively,  by  means  of  a  cabinet 
of  small  storage  cells,  and  thus  to  serve  as  electrodes 
for  the  application  of  an  electrostatic  field. 

In  this  way  the  positive  particles  can  be  sub- 
jected at  the  same  time  to  a  magnetic  and  an  electric 
field.  It  will  be  noticed  that,  whereas  in  the  case  of 
the  cathode  ray  experiments  described  in  an  earlier 
chapter  the  two  fields  were  at  right  -angles  to  each 
other,  in  this  case  the  two  fields  are  parallel,  and  the 
corresponding  deflections  therefore  at  right  angles 
to  each  other. 

After  passing  through  these  fields,  the  rays  fall 
either  upon  the  glass  plate  Z,  which  is  covered  with 
powdeied  willemite,  or  upon  a  photographic  plate, 
which  can  be  introduced  when  required  immediately 
in  front  of  Z  by  suitable  devices. 

The  side  tube  L  leads  to  a  tube  filled  with  char- 
coal and  immersed  during  the  experiment  in  liquid 
air,  a  device  due  originally  to  Sir  James  Dewar  for 
absorbing  as  completely  as  possible  the  gases  in  this 


46  MOLECULAR  PHYSICS 

part  of  the  apparatus.  This  detail,  apparently 
insignificant  in  itself,  has  had  much  to  do  with  the 
success  of  the  method.  If  the  gas  in  the  camera  is 
at  the  pressure  most  suitable  for  the  production  of 
positive  rays  in  the  discharge  tube,  the  effects 
observed  on  the  screen  are  found  to  be  almost 
entirely  secondary.  The  residual  gas  in  the  camera 
becomes  strongly  ionized  by  the  action  of  the 
positive  rays  upon  it.  The  latter  are  thus  travelling 
through  an  atmosphere  charged  with  negative 
electrons,  with  which  they  readily  combine  to  form 
neutral  molecules  again.  When  this  has  taken  place, 
the  particle  is  no  longer  acted  upon  by  electric  or 
magnetic  fields.  The  exact  extent  of  its  deflection 
will  depend  upon  the  length  of  time  during  which  it 
succeeded  in  retaining  its  charge.  These  secondary 
effects  still  make  their  appearance  upon  some  of  the 
photographs  taken.  They  can,  however,  always  be 
detected  by  the  fact  that  they  either  disappear  or 
alter  in  position  or  appearance,  if  the  pressure  in  the 
camera  is  slightly  lowered  or  slightly  raised. 

The  charcoal  and  liquid  air  method  enables  us  to 
remove  the  residual  gas  so  rapidly  that  it  is  possible 
to  have  the  pressure  in  the  camera  considerably 
lower  than  that  in  the  discharge  tube,  the  diffusion 
along  the  long  narrow  copper  tube,  which  is  their 
only  connection,  being  comparatively  slow.  In  this 
way  the  production  and  the  measurements  of  the 
particles  can  both  be  carried  on  under  the  most 
favourable  conditions. 

Let  us  consider  the  course  of  the  positive  particle 
from  its  genesis  in  the  discharge  tube  to  its  stoppage 
on  the  photographic  plate.  Particles  formed  near 
the  anode  will  fall  through  practically  the  whole  of 
the  difference  of  potential  between  the  electrodes  of 
the  discharge  tube,  some  30,000  or  40,000  volts. 
The  energy  they  acquire  will  thus  be  V  X  E  where  V 
is  this  difference  of  potential,  and  E  the  charge  on 


THE  NEW  METHOD  OF  ANALYSIS   47 


the    particle.      Their   velocity  v,  on   reaching    the 
cathode,  will  thus  be  given  by  j"- 


This  is  the  maximum  velocity  the  particles  can 


X n 


K 


0 


N 

X 


\ 


\ 


\ 


\ 


FIG.  10. — POSITIVE  RAY  PARABOLAS. 

attain.  Those  commencing  their  existence  nearer 
the  cathode  than  this,  only  fall  through  a  fraction  of 
the  full  potential  V,  and  thus  acquire  only  a  fraction 
of  this  maximum  velocity.  Thus,  the  stream  of  rays 


48  MOLECULAR  PHYSICS 

passing  through  the  cathode  will  contain  particles 
moving  with  all  velocities  up  to  a  certain  maximum. 
On  passing  into  the  electric  and  magnetic  fields 
at  MN  they  will  be  acted  upon  by  forces  equal  to 
XE  and  HE?;  respectively  where  X  is  the  electric 
and  H  the  magnetic  field,  exactly  as  in  the  case  of  the 
cathode  particles,  the  only  difference  being  that  the 
directions  of  the  deflections  will  be  in  the  opposite 
directions  to  those  of  the  negative  particles.  It  can 
be  shown*  that  these  forces  will  cause  the  point 
at  which  the  particle  strikes  Z  to  be  deflected  through 

HE 

distances  equal  to  ki  --  in  the  case  of  the  magnetic 
mv 

XE 

field,  and  k2  —  *  in  tne  case  °f  tne  electric  field,  ki 
2 


and  &2  being  constants  which  depend  only  on  the 
relative  dimensions  of  the  various  parts  of  the 
apparatus.  It  must  be  remembered  that  the  fields 
have  been  so  disposed  that  these  two  deflections 
will  take  place  at  right  angles  to  each  other. 

Thus  if  O  (Fig.  10)  represents  the  position  on 
the  plate  of  the  undetected  rays,  and  OX,  OY  are 
the  directions  of  the  electric  and  magnetic  deflec- 
tions, the  particle  after  passing  through  the  two 
fields,  will  be  deflected  to  some  point  P  such  that 

PK  =  x  =  k*  ^       (electric  deflection)      .     (a) 

PJ  =  y  =  ki  5^       (magnetic  d 
We  see  from  these  equations  that 


PJ  =  y  =  ki  (magnetic  deflection)  .     (b) 


Thus,  if  the  strengths  of  the  two  fields  are  kept 

*  Appendix  A. 


THE  NEW  METHOD  OF  ANALYSIS  40 

the  same  throughout  the  experiment,  all  the 
quantities  within  the  brackets  will  be  constant. 
Thus,  y/x  will  be  a  measure  of  the  velocity  of  the 
deflected  particle,  while  the  ratio  y2/x  will  measure 
the  ratio  of  the  mass  to  the  charge. 

If  all  the  particles  were  identical,  and  had  the 
same  velocity,  the  spot  O  would  simply  be  shifted 
to  the  point  P.  As  we  have  seen  the  velocities  of 
the  particles  vary  considerably.  The  rays  will 
therefore  not  be  deflected  to  a  single  spot,  even  if 
their  mass  and  charge  are  identical,  but  will  be 
drawn  out  into  a  line  or  band.  By  equation  (d) 
all  the  particles  for  which  m/E  is  the  same  will, 
however,  lie  on  some  curve  for  which  the  value  of 
y*/x  is  constant  ;  such  a  curve  is  known  as  a  parabola. 

If  the  particles  emerging  from  the  cathode  con- 
sist of  atoms  of  differing  atomic  weight,  they  will  be 
sorted  out  into  a  series  of  parabolas  one  above  the 
other,  each  curve  corresponding  to  some  definite 
value  of  m/Mt.  Since  the  velocity  which  is  propor- 
tional to  y/^  cannot  exceed  a  certain  value,  these 
curves  will  not  be  complete,  but  will  stop  short  at 
some  definite  distance  from  the  axis  O  Y.  The  appear- 
ance of  the  plate  after  exposure  should  therefore  be 
somewhat  as  shown  in  the  top  left  hand  quadrant 
Fig.  10,  where  two  such  parabolas  are  shown. 

To  measure  the  curves,  drop  any  perpendicular 
on  OXrcutting  the  curves  in  /  and  m,  and  the  axis  in 
n.  Then,  from  equation  (b)  it  can  be  seen  that 


since  the  value  of  x  is  the  same  for  all  points  along 
the  line  Imn.  Thus,  if  EX  =  E2,  that  is  to  say,  if  the 
two  particles  carry  the  same  charge,  the  ratio  of  the 
masses  of  the  two  sets  of  particles  is  simply  equal  to 


The  line  OX  has  no  real  existence  on  the  plate, 
but  the  apparatus    can    be    arranged   so  that  the 
M.P.  4 


50  MOLECULAR   PHYSICS 

direction  of  the  deflections  are  parallel  to  the 
edges  of  the  photographic  plate,  while  the  position 
of  O  is  always  marked  by  a  very  bright  spot 
caused  by  rays  which  come  through  the  cathode 
uncharged,  and  are  therefore  undeflected.  A  more 


FIG.  ii. — PARABOLAS  DUE  TO  MULTIPLE-CHARGED 
MERCURY  ATOMS. 

accurate  method  is  to  reverse  the  field  halfway 
through  the  exposure.  The  direction  of  the 
deflection  is  thus  reversed,  and  symmetrical  para- 
bolas are  formed  on  the  opposite  side  of  OX  as 
shown  in  Fig.  10.  The  distance  between  the  two 
branches  of  the  same  curve  is  then  twice  the  distance 
of  either  from  the  line  OX. 


THE  NEW  METHOD  OF  ANALYSIS  51 

It  will  have  been  noted  that  the  ratio  of  the 
squares  on  these  ordinates  does  not  give  directly 
the  ratio  of  the  masses  of  the  particles,  but  only 
the  ratio  of  what  we  may  term  their  electrochemical 
equivalents.  Fortunately,  however  the  majority 


FIG.  12. — TYPICAL  POSITIVE  RAY  PHOTOGRAPH. 

of  the  particles  carry  the  single  electronic  charge  ey 
while  in  any  case  the  charge  E  on  the  positive  particle 
cannot  be  more  than  a  small  integral  multiple  of 
this.  Very  little  uncertainty  is  as  a  rule  introduced 
from  this  cause,  though  it  does  occasionally  arise. 
Mercury  is  the  greatest  offender  in  this  respect,  as 

4—2 


MOLECULAR   PHYSICS 


mercury  atoms  carrying  as  many  as  eight  charges 
are  sometimes  to  be  detected.  Thus,  five  of  the 
six  parabolas  on  Fig.  n,  which  is  reproduced  from 
one  ol  Prof,  Thomson's  photographs,  are  due  to 
atoms  of  mercury,  carrying  respectively  one,  two, 

TABLE  III. 

Atmospheric  nitrogen.  Potential  across  discharge  tube, 
30,000  volts  ;  current  through  magnet,  3*5  amperes  ; 
potential  difference  in  electric  field,  200  volts. 


M 

WE. 

Probable  cause  of  line. 

7-2 

2OO 

Hg  + 

Mercury  atom  with  single 

charge. 

10*3 

IOO 

Hg+  + 

Mercury    atom    with    two 

charges. 

12-4 

67 

Hg+  + 

-f-    Mercury  atom  with  three 

charges. 

IT4 

44 

CO2  + 

Molecule  of  carbon  dioxide. 

16-5 

TT 

39 

A  + 

Argon     atom      (40)      with 

* 

single  charge. 

19*4 

28 

No  + 

Nitrogen     molecule     with 

single  charge1. 

2VI 

20 

Ne  + 

?  Neon  with  single  charge. 

J 
25-6 

0  f 

Atom  of  oxygen  with  single 

• 

charge. 

27-6 

14 

N  + 

Nitrogen  atom;  with  single 

/ 

charge. 

3O'O 

12 

C  -f- 

Carbon   atom   with   single 

»} 

charge.           j 

38-7 

7 

N  +  + 

Nitrogen    atom    with    two 

*J        / 

/ 

charges. 

three,  four,  and  eight  charges.  The  latter  line, 
though  clear  on  the  negative,  is  too  faint  to  show 
up  clearly  in  the  reproduction. 

The    measurement    and    interpretation    of    the 
results  can  best  be  illustrated  by  an  actual  example. 


THE  NEW  METHOD  OF  ANALYSIS  53 

Fig.  12  represents  a  fairly  typical  photograph 
obtained  with  the  apparatus.  The  gas  in  the 
discharge  tube  in  this  case  was  atmospheric  nitrogen, 
that  is  to  say,  air  from  which  the  oxygen  had  been 
extracted.  Table  III.  contains  the  actual  measure- 
ments made  on  this  plate. 

The  first  column  gives  the  distance  of  the  different 
parabolas  from  the  axis  OX,  measured  along  some 
common  ordinate  as  explained  above.  The  second 
column  gives  the  value  deduced  from  these  figures 
for  the  relative  masses  of  the  particles,  assuming 
that  they  all  carry  the  same  charge.  If  the  charge 
carried  is  double  or  treble  this  value,  the  corre- 
sponding mass  so  obtained  Will  be  half,  one-third 
and  so  on,  of  the  actual  mass  of  the  particle.  The 
standard  line  on  this  plate  was  the  innermost  one 
of  all,  which  as  its  appearance  shows,  is  due  to 
mercury  carrying  a  single  charge.  The  mass  of  this 
particle  is  for  convenience  taken  as  being  equal  to 
its  atomic  weight  (200). 

Examining  the  table,  it  will  be  seen  that  the  three 
inner  parabolas  represent  particles  having  a  value  of 
m/E  of  200,  \  .  (200),  and  £  (200).  They  are  due 
to  mercury  atoms  having,  respectively,  one,  two,  and 
three  charges.  Mercury  vapour  is  always  present 
in  the  tube  unless  special  precautions  are  taken  to 
exclude  it,  as  it  is  used  in  the  vacuum  pumps 
attached  to  the  apparatus.  The  next  line  is  made 
by  particles  having  a  mass  of  44  ;  these  are  singly 
charged  molecules  of  carbon  dioxide  ;  carbon  com- 
pounds being  usually  present  as  impurities  in  small 
quantities. 

The  argon  line  (39)  is  the  long  bright  parabola, 
immediately  below  the  very  thick  bright  line  (28), 
due  to  molecules  of  nitrogen  with  a  single  positive 
charge.  This,  as  might  be  expected,  is  the  brightest 
line  in  the  photograph.  The  parabola  for  which  d 
is  23  .  i,  is  very  faint  on  the  reproduction.  It 


54  MOLECULAR  PHYSICS 

probably  represents  Neon  (20)  though  there  is  also  the 
possibility  that  it  is  formed  by  argon  atoms  with  a 
double  charge,  as  the  argon  line  (40)  is  very  bright. 


FIG.  13. — POSITIVE  RAY  PARABOLAS. 

Our   method    does    not    enable    us    to    distinguish 
between  these  alternatives. 

The  triplet  of  lines  which  follow  is  due  to  atoms 
of  oxygen,  nitrogen,  and  carbon.  The  last  line  on 
the  plate,  indicating  a  value  7  is  the  nitrogen  atom 
with  a  double  charge.  The  hydrogen  line  which  is 


THE  NEW  METHOD  OF  ANALYSIS  55 

nearly  always  present,  has  been  deflected  entirely 
off  the  plate  by  the  large  magnetic  field  applied  in 
order  to  separate  the  heavier  constituents. 

It  will  thus  be  seen  that  all  the  lines  on  our  plate 
correspond  to  elements  which  we  might  expect  to  find 
present  from  the  nature  of  the  gas  employed.  There 
are  no  lines  unexplained,  and  the  values  obtained 
for  the  relative  masses  of  the  particles  correspond 
very  closely  to  the  atomic  and  molecular  weights 
determined  from  chemical  considerations. 

The  faint  lines  seen  on  Fig.  12  joining  some  of 
the  parabolas  to  the  origin,  are  due  to  the  secondary 
effects  which  we  have  already  mentioned.  The 
mercury  parabolas,  however,  as  will  be  seen  from 
the  figure,  do  actually  extend  to  within  a  very  short 
distance  of  the  origin.  This  is  due  to  quite  a 
different  cause.  Turning  back  to  equation  (a),  it 
will  be  seen  that  the  electric  deflection  is  propor- 
tional to  the  charge  EI  carried  by  the  particle  in  the 
electric  field  divided  by  %mv2,  the  kinetic  energy  of 
the  particle.  We  have  seen  that  the  maximum 
value  of  the  latter  is  equal  to  V .  E2,  where  V  is  the 
potential  of  the  discharge,  and  E2  the  charge  carried 
by  the  particle  in  the  discharge  tube.  The  minimum 
value  of  the  electric  deflection,  that  is  to  say,  the 
nearest  point  to  which  the  parabolas  can  extend 
will  be  proportional  to  Ej/E2  and  will  thus  be  the 
same  for  all  particles,  whatever  their  mass  and 
charge,  if  each  particle  carries  the  same  charge  in  the 
tube  as  in  the  camera.  Thus  all  the  curves  will 
stop  short  at  a  certain  line  drawn  parallel  to  OY. 
This  is  well  shown  in  Figs.  13  and  14. 

If,  however,  a  particle  in  the  discharge  tube 
having  a  double  or  treble  charge,  loses  one  or  more 
of  these  extra  charges  before  the  electric  field  at  MN 
is  reached,  the  value  of  E2/Ei  will  be  greater  than 
unity,  and  the  parabola  will  extend  further  towards 
the  axis  OY. 


56  MOLECULAR  PHYSICS 

These  extensions  of  the  parabolas  are  very 
clearly  shown  in  the  three  inner  curves  of  Fig.  13, 
where  an  almost  complete  break  occurs  between  the 
termination  of  the  original  parabola  and  its  con- 
tinuation by  particles  which  have  parted  with  one 
of  their  original  charges.  These  three  parabolas  are 
due  respectively  to  Mercury  (200),  Xenon  (132),  and 
Krypton  (83).  The  two  outer  curves,  representing 


FlG.    14. — GAS    EVOLVED    FROM    PLATINUM. 

Argon  (40)  and  the   Nitrogen  molecule    (28),   end 
abruptly  at  the  normal  distance  from  OY. 

The  best  example  of  the  effect  is,  however,  shown 
by  the  mercury  lines  in  Fig.  n.  The  normal 
mercury  atom  in  the  discharge  tube  apparently 
carries  a  charge  of  8e,  and  approaches  the  cathode 
with  an  amount  of  energy  equivalent  to  this.  The 
innermost  mercury  parabola  (Fig.  n)  gives  a  value 
for  the  mass  just  200  times  that  of  the  hydrogen 
atom.  It  is  therefore  due  to  a  mercury  atom  carry- 
ing a  unit  charge,  and  having  thus  only  one-eighth 


THE  NEW  METHOD  OF  ANALYSIS  57 

of  the  charge  it  carried  in  the  discharge  tube.  The 
value  of  Ei/E2  is  thus  |  and  the  parabola  extends  to 
one-eighth  of  the  usual  minimum  distance  from  the 
vertical  axis.  The  next  line  (m  =  100)  is  due  to 
atoms  with  two  charges,  and  extends  to  one-quarter 
of  the  usual  minimum  distance,  and  so  on,  until  the 
last  parabola  which  corresponds  to  a  mercury  atom 
with  eight  charges  (the  same  number  as  in  the  dis- 
charge), ends  up  at  the  usual  distance  from  the  axis. 

This  gradual  shortening  of  the  parabolas  for  the 
differently  charged  mercury  atoms,  is  beautifully 
shown  in  Fig.  n,  where  the  terminations  of  the  five 
mercury  parabolas  can  be  seen  to  lie  exactly  on  a 
straight  line  through  the  point  O  inclined  at  an  angle 
to  OY,  as  would  be  expected  on  the  above  theory. 

It  will  be  noticed  that  the  lines  decrease  in 
intensity  as  the  number  of  charges  carried  is 
increased.  This  is  always  to  be  observed  on  the 
photographs,  and  is  a  fact  which  sometimes  helps 
us  to  the  right  interpretation  of  a  doubtful  line  in 
a  photograph.  For  example,  if  the  line  indicating 
a  mass  of  20  on  Fig.  12  had  been  brighter  than  the 
Argon  line  (40)  we  should  have  been  able  to  say 
definitely  that  it  was  due  to  atoms  of  Neon,  and  not 
to  Argon  atoms  with  a  double  charge. 

The  plates  so  far  described  were  all  taken  using 
large  magnetic  fields  in  order  to  obtain  a  suitable 
dispersion  of  the  heavier  atoms.  The  last  plate  of 
the  series  (Fig.  14)  was  taken  with  a  smaller  magnetic 
dispersion,  and  shows  the  lines  due  to  some  of  the 
lighter  elements.  It  is  of  peculiar  interest  at  the 
present  moment,  as  it  is  one  of  the  photographs 
which  shows  the  mysterious  line  due  to  particles  for 
which  the  ratio  of  the  mass  to  the  charge  is  exactly 
three  times  that  for  the  singly  charged  hydrogen 
atom.  On  this  account  it  may  perhaps  be  of 
interest  to  give  the  actual  measurements  made  on 
this  plate  (Table  IV.).  The  first  column  of  the 


MOLECULAR  PHYSICS 


table  gives  the  actual  measurements  of  a  common 
ordinate  of  the  different  parabolas,  the  second 
column  the  corresponding  values  of  m/E,  the  ratio 
for  the  hydrogen  atom  being  taken  as  unity. 

The  gas  used  in  the  experiment  was  a  sample  of 
that  mysterious  gas  which  is  evolved  in  considerable 
quantities  when  any  metal  is  heated,  or  better  still, 
as  in  the  present  case,  bombarded  with  cathode  rays 
in  a  vacuum  tube.  That  gases  were  evolved  under 
these  circumstances  had  been  known  for  some 
considerable  time,  but  their  analysis  had  not  been 


Gases    evolved   from 
rays  for  6  hours. 


TABLE  IV. 

Platinum  bombarded 
(See  Fig.  14.) 


with  Cathode 


d  m.m. 

;«/E. 

Probable  cause  of  line. 

27'O 

I'OO 

H    +  Hydrogen  atom. 

19-1 

2'O 

H2  -j-  Hydrogen  molecule. 

15-6 

3-0 

?       Unknown  element. 

7-8 

12 

C     +  Carbon  atom. 

6-7 

16 

O    +  Oxygen  atom. 

5*8 

21 

Ne  +  Neon  atom  (20). 

4-8 

32 

O2   +  Oxygen  molecule. 

previously  effected.  As  will  be  seen  from  the  table, 
the  gas  consists  principally  of  hydrogen,  but  helium 
and  neon  are  also  present ;  while  the  plate  also  shows 
traces  of  carbon  and  oxygen,  probably  due  to 
impurities  in  the  apparatus. 

In  addition  to  these  known  substances  there  is 
also 'very  clearly  marked  a  line,  the  third  from  the 
top  of  the  plate,  which  cannot  be  assigned  to  any 
known  element  or  compound.  There  was  at  first 
the  possibility  that  it  might  be  due  to  a  carbon  atom 
carrying  four  elementary  charges,  but  this  hypothesis 
was  found  to  be  untenable.  In  the  first  place  the 


THE  NEW  METHOD  OF  ANALYSIS  59 

line  under  consideration  is  much  brighter  than  that 
due  to  the  singly  charged  carbon  atoms,  while  we 
have  seen  that  on  a  given  plate  the  curves  due  to 
multiply  charged  atoms  are  invariably  fainter  than 
those  due  to  atoms  of  the  same  substance  having  a 
single  charge.  In  the  second  place,  when  pre- 
cautions were  taken  to  exclude  carbon  compounds 
from  the  apparatus  the  carbon  line  (12)  completely 
disappeared,  while  the  line  3  remained  as  bright  as 
ever. 

Only  two  possibilities  remain.  The  line  may  be 
due  to  a  previously  unknown  element  of  atomic 
weight  3,  or  it  is  due  to  a  hitherto  unknown  modifica- 
tion of  hydrogen  H3  corresponding  to  ozone.  If  the 
latter  is  the  case,  the  substance  has  some  quite  unex- 
pected properties,  as  it  is  certainly  not  destroyed  by 
sparking  with  excess  of  oxygen.  Professor  Sir  J.  J. 
Thomson  is  still  actively  pursuing  his  experiments  on 
this  substance,  and  some  very  interesting  results 
may  be  expected.  Until  these  experiments  are 
completed  it  would  be  premature  to  venture  any 
further  opinion  as  to  the  real  nature  of  this  new  gas. 

Another  parabola  which  is  found  when  the  gases 
from  liquid  air  residues  are  introduced  into  the  tube 
suggests  interesting  possibilities.  This  is  a  line 
giving  a  value  for  w/E  equal  to  22.  This  might 
possibly  be  a  molecule  of  carbon  dioxide  (44)  with  a 
double  charge,  but  from  the  fact  that  it  appears  only 
in  these  mixtures  of  the  rarer  atmospheric  gases, 
and  that  it  is  quite  well  marked  even  when  the 
CO2  and  CO  lines  are  absent  seems  to  point  to  it 
being  a  new  compound  NeH2  of  neon  and  hydrogen. 

A  few  further  points  of  interest  in  the  photo- 
graphs may  be  noted.  The  bright  central  spot 
shown  in  all  the  figures  is  due  to  the  particles  which 
have  lost  their  charge  during  their  passage  through 
the  long  copper  canal  tube,  and  are  therefore  unde- 
flected  by  any  combination  of  electric  and  magnetic 


60  MOLECULAR   PHYSICS 

fields.  The  atoms  of  some  elements  have  such 
a  strong  attraction  .  for  the  surrounding  negative 
electrons  that  they  actually  take  up  more  of  them 
than  would  be  sufficient  to  neutralise  the  original 
positive  charge.  They  thus  enter  the  deflecting 
fields  with  a  negative  instead  of  a  positive  charge, 
and  so  give  rise  to  parabolas  in  the  opposite  quadrant 
to  those  due  to  the  positive  particles,  but  giving,  of 
course,  the  same  values  for  m/'E.  At  least  two  of 
these  "  negative "  parabolas  appear  on  Fig.  13. 
Oxygen  and  the  halogens  if  present  in  any  quantity 
almost  invariably  give  these  negative  curves, 
Strangely  enough  hydrogen,  which  is  generally 
reckoned  among  the  more  electro-positive  elements, 
also  frequently  shows  the  same  effect.  It  has  never 
been  found  with  nitrogen  or  helium. 

We  have  so  far  only  been  considering  the  relative 
values  on  the  ratio  m/E  for  the  different  particles. 
By  measuring  the  dimensions  of  the  different  parts 
of  the  apparatus  and  calculating  the  actual  values 
of  the  constants  ki  and  &2,  the  absolute  value  of  this 
ratio  for  any  given  parabola  can  be  deduced.  Such 
a  determination  was  made  by  Professor  Sir  J.  J. 
Thomson,  and  it  was  found  that  the  absolute  value 
for  the  outermost  parabola  of  all  was  almost  exactly 
io~4.  We  have  seen  that  this  is  the  value  of  the 
ratio  for  a  hydrogen  ion  in  solution  or  a  hydrogen 
atom  carrying  a  single  charge.  The  particles  with 
which  we  have  been  dealing  are  therefore  actual 
atoms  and  molecules  of  the  substances  in  the 
discharge  tube,  as  we  have  tacitly  assumed  in  the 
foregoing  pages. 

We  have  now  described  in  some  detail  the  prin- 
cipal features  of  the  new  method  of  molecular 
analysis.  Its  importance  can  hardly  be  exaggerated. 
In  the  first  place  it  enables  us  to  detect  with  certainty 
the  presence  in  a  gaseous  mixture  of  far  smaller 
quantities  of  an  element  than  could  be  accomplished 


THE  NEW  METHOD  OF  ANALYSIS  61 

by  any  other  method  known  to  science.  Professor 
Thomson  has  given  the  following  striking  illustration 
of  the  delicacy  of  the  method.  It  was  found  that  the 
photographs  taken  with  atmospheric  argon  in  the 
apparatus  always  showed  the  helium  line  faint  but 
quite  distinct.  In  this  particular  experiment  the 
volume  of  the  discharge  tube  was  about  2  litres, 
and  the  pressure  of  the  gas  in  the  tube  1/300  m.m.  of 
mercury.  The  gas  experimented  on  would  therefore 
have  had  a  volume  of  about  i/ioo  c.c.  at  atmospheric 
pressure.  This  is  approximately  the  quantity  of 
argon  in  i  c.c.  of  air  at  atmospheric  pressure.  We 
are  thus  able  to  detect  the  helium  present  in  a  single 
cubic  centimetre  of  air.  According  to  the  deter- 
minations of  Professor  Ramsay  this  amounts  to  no 
more  than  four  millionths  of  a  cubic  centimetre. 

The  new  method  has  the  further  advantage  over 
spectroscopic  analysis  that  it  gives  directly  the 
atomic  or  molecular  weight  of  the  substance  under 
experiment.  Thus  the  photograph  of  Fig.  14  not 
only  reveals  the  existence  of  a  new  gas  but  gives  at 
once  its  molecular  weight. 

Lastly,  and  this  is  perhaps  most  important  of 
all  from  the  point  of  view  of  an  intimate  study  of 
the  modes  and  methods  of  chemical  combination 
and  decomposition,  the  time  taken  for  each  single 
particle  to  register  its  presence  and  mass  is 
exceedingly  minute.  A  very  moderate  value  for 
the  speed  of  the  positive  particles  is  io8  cms.  per 
second  (about  620  miles  per  second).  Their  path 
in  the  discharge  tube  is  not  more  than  50  cms.  in 
all.  Thus  a  particle  when  caught  by  the  discharge 
will  register  itself  on  the  photographic  plate  in 
considerably  less  than  one  millionth  of  a  second. 

We  might  therefore  reasonably  expect  to  find  on 
the  photographs  curves  corresponding  to  temporary 
combinations  of  atoms  so  unstable  that  their  whole 
period  of  existence  is  not  greater  than  one  millionth 


62  MOLECULAR  PHYSICS 

of  a  second,  if  any  such  combinations  are  formed  in 
the  discharge  tube.  Thus  in  the  case  of  chemical 
reactions  taking  place  within  the  discharge  tube  we 
might  expect  to  find  on  the  plate  traces  not  merely 
of  the  stable  products  of  the  reaction  but  also  of 
any  intermediate  stages  occurring  in  the  course  of 
the  reaction.  The  field  thus  opened  up  for  an 
intimate  study  of  the  mechanism  of  chemical 
reactions  is  illimitable. 

Though  little  has  as  yet  been  accomplished  along 
these  lines,  the  experiments  already  made  show  that 
this  expectation  is  not  unfounded.  As  a  very  simple 
illustration  of  the  application  of  the  method  we  may 
take  the  case  of  phosgene,  COC12.  When  this  was 
introduced  into  the  apparatus  the  photographs 
showed  that,  in  addition  to  the  molecules  of  unde- 
composed  phosgene  (99),  the  carriers  of  positive 
electricity  were  molecules  of  carbon  monoxide  (28) 
and  atoms  of  chlorine  (35*5).  The  lines  due  to 
single  atoms  of  carbon  and  oxygen  were  very  faint 
indeed,  thus  showing  that  the  decomposition"  of  the 
compound  by  the  discharge  consisted  of  the  separa- 
tion of  the  chlorine  atoms  from  the  CO  molecule, 
the  bond  between  the  carbon  and  oxygen  atoms 
remaining  intact. 

This  is  a  simple  case  where  the  results  obtained 
might  easily  have  been  predicted.  Another  inter- 
esting case  is  that  of  methane,  CH4.  When  this  gas 
is  subjected  to  the  discharge  a  group  of  five  lines 
appears  on  the  photographic  plate,  indicating  the 
presence  of  particles  having  masses  12,  13,  14,  15  and 
16  times  that  of  the  hydrogen  atom.  These  corre- 
spond to  particles  having  the  composition  C,  CH, 
CH2,  CH3,  and  CH4  respectively. 

We  have  been  dealing  so  far  with  the  many 
advantages  of  the  method.  Some  of  its  limitations 
should  perhaps  be  pointed  out.  In  the  first  place 
the  substance  to  be  exeprimented  on  must  be  either 


THE  NEW  METHOD  OF  ANALYSIS  63 


gaseous  or  capable  of  exerting  a  vapour  pressure  at 
ordinary  temperatures.  A  more  important  defect, 
and  one  which  is  shared  by  the  spectroscopic  method, 
is  that  an  element  may  be  present  in  considerable 
quantity  in  the  discharge  tube  without  producing  a 
corresponding  trace  upon  the  photographic  plate. 
Thus,  although  many  metals  have  compounds  suffi- 
ciently volatile  for  the  purpose  of  the  experiment, 
mercury  and  nickel  are  the  only  metallic  elements 
which  have  so  far  been  detected  by  the  method. 

One  word  may  be  added  as  to  the  relative  inten- 
sity of  the  different  lines  on  a  given  photograph. 


B 


tk 

FIG.  15. — APPARATUS  FOR  THE  ELECTRICAL  MEASUREMENT  OF 
THE  POSITIVE  RAYS. 

It  is  found  that  in  general  this  is  far  from  repre- 
senting the  actual  proportion  of  the  particles  in  the 
stream  having  masses  corresponding  to  the  different 
lines.  For  some  reason  at  present  unexplained,  a 
given  number  of  atoms  of  a  light  element  produce 
far  greater  effect  on  a  photographic  plate  or  wille- 
mite  screen  than  an  equal  number  of  the  atoms  of  a 
heavier  element.  Thus  the  parabola  corresponding 
to  the  hydrogen  atom  will  often  be  the  most  intense 
line  on  the  plate  when  the  amount  of  that  element 
present  forms  less  than  i%  of  the  contents  of  the 
tube. 


64  MOLECULAR  PHYSICS 

This  has  been  very  clearly  demonstrated  by 
Sir  J.  J.  Thomson  by  substituting  an  electrical  for 
a  photographic  method  of  detecting  the  positive 
particles.  It  must  be  remembered  that  as  all  the 
particles  with  which  we  are  dealing  carry  an  electric 
charge  they  can  be  measured  by  collecting  them  in 
a  Faraday  cylinder  in  the  way  described  for  the 
a-particles  in  the  preceding  chapter. 

To  carry  out  the  experiment  a  brass  plate  B 
(Fig.  15)  was  substituted  for  the  glass  screen  Z  of 
Fig.  9.  If  the  brass  plate  is  covered  with  powdered 
willemite  a  series  of  bright  parabolic  curves  will  of 
course  appear  upon  it  when  the  tube  is  running 
somewhat  as  indicated  in  Fig.  I5a,  where  three  such 
curves  are  shown.  If  a  slit  SS  is  cut  in  the  brass 
plate  so  as  to  coincide  with  one  of  the  parabolas  the 
particles  forming  this  parabola  will  pass  through  the 
slit  and  can  be  collected  by  a  Faraday  cylinder  F 
(Fig.  I5b)  placed  immediately  behind  it.  As 
explained  in  Chapter  III.,  the  rate  of  charging  up 
of  an  electrometer  connected  to  the  Faraday 
cylinder  will  be  proportional  to  the  number  of 
particles  entering  the  latter  per  second,  that  is  to 
say,  to  the  relative  number  of  molecules  in  the 
positive  rays  which  have  a  mass  corresponding  to 
that  indicated  by  the  parabola  coinciding  with  the 
slit  SS. 

If  the  slit  could  be  made  to  coincide  successively 
with  each  of  the  different  parabolas  indicated  by  the 
glowing  willemite,  the  relative  rates  of  deflection  of 
the  electrometer  for  the  different  positions  would  be 
proportional  to  the  number  of  particles  of  corre- 
sponding mass  in  the  positive  rays  from  the  discharge. 
The  experiment  can  be  performed  much  more 
conveniently  without  moving  the  slit  by  varying  the 
intensity  of  the  deflecting  magnetic  field,  H.  If  this 
is  increased  it  can  easily  be  seen  that  the  corre- 
sponding magnetic  deflections  of  the  particles  will 


THE  NEW  METHOD  OF  ANALYSIS  65 

also.be  increased  and  the  various  parabolas  will  move 
outwards  from  the  centre  of  the  screen.  In  this  way 
each  of  them  in  turn  can  be  brought  to  coincide  with 
the  parabolic  slit  SS.  It  can  easily  be  seen  from 
equations  (a)  and  (b)  that  if  the  other  conditions  of  the 
experiment  remain  the  same  the  value  of  m/E  for  a 
given  set  of  particles  is  proportional  to  the  square 
of  the  strength  of  the  magnetic  field  necessary  to 
deflect  them  to  a  given  position.  Thus  from  the 
various  rates  of  deflection  of  the  electrometer 
corresponding  to  different  values  of  the  magnetic 
field  we  can  at  once  determine  the  relative 
number  of  particles  in  the  beam  of  positive  rays 
corresponding  to  definite  values  of  the  ratio  w/E. 
In  other  words,  we  can  determine  the  relative  pro- 
portions of  the  different  kinds  of  atoms  and 
molecules  which  make  up  a  given  beam  of  positive 
rays. 

On  making  the  experiment  it  was  found  that 
there  was  practically  no  movement  of  the  needle  of 
the  electrometer  connected  to  the  Faraday  cylinder 
except  when  one  ol  the  bright  parabolas  was  made 
to  coincide  with  the  slit.  If  a  fairly  narrow  slit  was 
used,  the  appearance  and  disappearance  of  a  deflec- 
tion of  the  electrometer  as  such  a  line  passed  across 
the  slit  was  surprisingly  sharp,  and  lines  quite  close 
together  could  easily  be  separated. 

Although  we  can  thus  perform  a  quantitative 
analysis  of  the  beam  of  positive  rays  it  cannot  be 
assumed  without  further  experiment  that  the 
number  of  atoms  of  an  element  in  the  beam  is 
necessarily  proportional  to  the  quantity  of  the 
substance  present  in  the  discharge  tube.  Preli- 
minary experiments,  however,  seem  to  indicate  that 
this  is  very  approximately  the  case  at  any  rate  for 
the  non-metallic  elements.  If  so,  this  latest  modifi- 
cation of  the  method  of  molecular  analysis  will 
enable  us  to  carry  out  not  merely  a  qualitative  but 
M.P.  5 


66  MOLECULAR   PHYSICS 

also  a  quantitative  analysis  of  any  gas  introduced 
into  the .  discharge  tube.  The  quantitative  deter- 
mination of  traces  of  a  gaseous  substance  too  small 
to  be  detected  by  the  spectroscope  will  then  have 
become  an  accomplished  fact. 


\ 


CHAPTER   V. 

THE  NATURE  AND  SIZE  OF  AN  ELECTRON. 

WE  must  now  turn  from  these  triumphs  of 
experimental  skill  to  some  theoretical  considerations, 
and  discuss  briefly  the  new  views  of  the  atom  to 
which  they  have  given  rise.  It  would  be  idle  to 
pretend  that  we  have  as  yet  any  theory  of  the 
structure  of  the  atom  which  absolutely  and  com- 
pletely sums  up  all  the  known  phenomena  of  Science. 
The  scientific  philosophers  of  an  earlier  age  hoped 
that  at  no  very  distant  date  they  might  be  able  to 
include  in  one  or  more  ponderous  tomes  all  that 
could  be  known  in  the  realm  of  physical  phenomena. 
Looking  down  the  long  vistas  which  the  new  dis- 
coveries have  so  recently  opened  up,  we  expect  no 
such  immediate  end.  We  are  not  yet  within 
sight  of  a  mechanical  or  electrical  theory  of  the 
universe  wherein  all  the  chemical  and  physical  pro- 
perties of  the  material  universe  shall  be  explicable 
in  terms  of  the  electrons  and  their  motions.  Still, 
while  wre  cannot  say  that  we  have  such  a  theory, 
there  are  certain  sign-posts  pointing  out  the  direction 
in  which  we  may  hope  for  ultimate  success.  Even 
now  it  is  possible  to  construct  "  models  "  of  the 
atom  which,  however  crude  and  insufficient  they 
may  be,  enable  us  to  link  together  many  most 
diverse  phenomena. 

In  the  realm  of  science  an  insufficient,  or  even  a 
false,  hypothesis  is  better  than  none  at  all,  and  it 
will  be  useful  to  take  the  best  approximation  we  can 
devise  to  serve  us  as  a  clue  through  the  labyrinth  of 

5—2 


68  MOLECULAR   PHYSICS 

experimental  facts  which  we  have  still  to  consider. 
At  the  same  time,  it  will  be  well  to  point  out  care- 
fully where  we  are  treading  the  solid  ground  of 
experimental  fact  and  legitimate  deduction,  and 
where  we  rise  to  the  higher  but  more  precarious 
flights  of  scientific  imagination. 

We  have  seen  that  electrons  are  contained  in  all 
atoms,  and  many  phenomena  lead  us  to  believe  that 
they  play  a  most  important  part  in  determining 
both  the  chemical  and  the  physical  properties  of  the 
substance.  The  question  naturally  arises,  what  is 
an  electron  ?  Fortunately  to  this  question  also  we 
are  able  to  give  some  answer.  An  electron  is  an 
atom  ,of  electricity  free  from  association  with  any- 
thing in  the  nature  of  matter  as  we  know  it.  It  not 
merely  has  a  charge,  it  is  a  charge,  and  apart  from 
its  charge  has  no  existence  and  no  properties,  not 
even  that  of  mass. 

The  exact  proof  of  this  statement  has  involved 
long  and  intricate  mathematical  analysis.  It  will, 
however,  be  possible,  without  going  at  all  deeply 
into  these  abstruse  calculations,  to  make  clear  the 
nature  of  the  proofs  advanced,  and  the  experimental 
evidence  upon  which  they  rest. 

In  the  first  place,  since  we  have  already  deter- 
mined the  mass  of  an  electron,  we  must  show  that 
such  a  moving  electric  charge  will  possess  mass,  a 
property  which  we  have  been  accustomed  to  associate 
only  with  what  we  call  matter.  The  proof  follows 
directly  from  the  ordinary  laws  of  electric  and  mag- 
netic induction,  and  was  first  given  by  Professor 
J.  J.  Thomson,  in  1881,  many  years  before  the  dis- 
covery of  the  electron  rendered  possible  any  practical 
application  of  the  result. 

Consider  a  small  sphere  charged  with  electricity 
of  either  sign  moving  through  space  with  a  velocity  v. 
We  have  already  pointed  out  that  this  moving  sphere 
will  be  equivalent  to  an  electric  current  element 


NATURE   AND   SIZE   OF   AN   ELECTRON    69 

coinciding  with  the  path  of  the  particle.  By  the 
usual  laws  of  electro-magnetic  induction  this  current 
element  will  produce  a  magnetic  field,  at  a  distance  r 
from  the  particle,  equal  to  ev  sin  0/r*,  where  6  is  the 
angle  between  the  direction  of  motion  of  the  particle 
and  the  direction  of  r.  Thus,  the  moving  particle  is 
surrounded  not  only  by  an  electro-static  field  due  to 
its  charge,  but  also  by  a  magnetic  field  due  to  the 
motion  of  that  charge.  It  will  be  seen  that  this 
field  has  its  greatest  value  in  a  direction  at  right 
angles  to  the  motion  of  the  particle,  and  falls  to  zero 
in  the  direction  in  which  the  particle  is  travelling. 

It  is  a  well-known  fact  that  a  magnetic  field  is 
the  seat  of  energy,  the  energy  in  a  field  of  strength  H 

H2 

being  ^—  times  the  volume.     The  magnetic  energy 

in  a  small  space  of  volume  u  at  a  distance  r  from  our 
moving  charge  is  thus 

(ev  sin  0\  2  u  ue1  sin  2#    0 


The  total  energy  of  the  magnetic  field  surround- 
ing the  particle  is  the  sum  of  the  energy  in  all  these 
little  volumes,  from  the  surface  of  the  particle  away 
to  infinity.  The  summation  of  this  quantity  does 


not  present  any  difficulties.      It  is  equal  to  ---  , 

where  a  is  the  radius  of  the  sphere. 

If  m   is   the   ordinary   mechanical   mass  of  the 
particle,  the  kinetic  energy  due  to  its  motion  will  be 

-  mv2.    In  addition  to  this  there  is,  as  we  have  shown, 

2 

a  quantity  of  energy  due  to  its  charge.     The  total 
energy  of  the  moving  particle  and  its  charge  is  thus 


I  mv*  + 1  — 

2  r  3    <*  ' 

1  /  2  £2\ 

If  we  write  this  in  the  form  —  ( m  +  -  -  )  v2,  and 

2  V          3  &  * 


70  MOLECULAR   PHYSICS 

compare  it  with  the  ordinary  Newtonian  expression 
for  the  kinetic  energy  of  a  particle  (-  mv*\  we  see 

that  the  particle  behaves  as  if  its  mass  m  had  been 

2  e2 

increased  by  an  amount  equal  to .     This  is  the 

3  a 

extra  or  "  electrical "  mass,  due  to  the  fact  that  the 

particle  carries  a  charge.     It  is  evident  that,  even 

if  m,  the  "  mechanical  "  mass  of  the  particle,  is  zero, 

the  "  electrical  "  mass  due  to  the  moving  charge 

will  still  persist.     Thus,  even  if  our  electron  is  a  pure 

charge  unassociated  with  any  mechanical  mass,  it 

will  still  have  an  electrical  mass  equal  to 

2  X  (electrical  charge)2 

3  X  radius. 

Since  this  "  electrical  "  mass  is  really  that  of  the 
magnetic  field  surrounding  the  particle,  it  resides 
not  in  the  particle  itself  but  in  the  medium  sur- 
rounding it,  that  is,  in  that  mysterious  fluid  which 
we  call  the  ether.  As  soon,  however,  as  we  attempt 
to  alter  the  motion  of  the  particle  this  energy  flows 
into  it  from  all  sides,  so  that,  as  far  as  experiments 
upon  the  particle  itself  are  concerned,  the  results 
obtained  are  precisely  the  same  as  if  it  resided 
permanently  there. 

To  make  this  somewhat  novel  idea  a  little  clearer 
we  may  consider  a  close  and  very  serviceable  analogy, 
where  the  mechanism  of  the  extra  mass  is  a  little 
clearer  than  in  the  electrical  case.  If  any  body  is 
moving  through  water,  or  any  viscous  fluid,  it  carries 
with  it  a  certain  amount  of  the  liquid  through  which 
it  is  moving.  In  the  case  of  a  sphere,  for  example, 
the  quantity  carried  along  by  the  motion  of  the  body 
amounts  to  half  the  volume  of  the  sphere  itself.  A 
long  cylinder  moving  at  right  angles  to  its  own  length 
will  carry  with  it  a  quantity  of  fluid  equal  to 
its  own  volume.  On  the  other  hand,  if  it  moves  in 
the  direction  of  its  own  length  the  fluid  entangled 


NATURE   AND   SIZE   OF   AN    ELECTRON    71 

is  practically  nil.  Thus,  in  order  to  set  the  body 
in  motion  with  a  velocity  v,  we  have  to  supply  to 
it  energy  enough  to  give  this  velocity,  not  only  to 
the  sphere  itself,  but  also  to  the  mass  of  fluid  which 
it  carries  with  it.  That  is  to  say,  if  M  is  the  mass  of 
the  sphere  itself,  and  M'  the  mass  of  the  attached 

fluid,  the  work  done  in  starting  the  body  is  -  (M +M')  .v2. 

In  other  words,  the  body  will  behave  as  if  its  mass 
were  increased  by  the  mass  of  the  fluid  entangled  by 
it.  Just  as  in  the  electrical  case,  this  extra  mass 
resides  in  the  surrounding  medium. 

It  makes  itself  apparent  at  the  surface  of  the 
sphere  when  the  motion  of  the  latter  is  altered  in 
any  way. 

We  may  very  profitably  extend  this  analogy 
further  in  that  part  of  our  proof  which  still  remains 
to  be  considered,  by  thinking  of  our  electric  field  in 
terms  of  tubes  of  electric  force.  This  conception  we 
owe  to  the  genius  of  Faraday.  Untrained  in  the 
methods  of  mathematicians,  he  found  the  mere 
algebraical  expression  for  the  laws  of  electrical 
attraction  both  unsatisfying  and  unstimulating. 
He  felt  that  if  two  bodies  attracted  each  other  it 
could  only  be  because  of  some  vital  bond  between 
them.  Thus  he  imagined  that  every  positive  charge 
was  the  beginning  of  a  certain  number  of  tubes  of 
force  stretching  out  through  space  until,  somewhere 
or  other,  they  ended  up  on  an  equal  but  opposite 
negative  charge. 

By  assuming  that  these  tubes  were  in  a  state  of 
tension  so  that  they  tended  to  shorten  themselves 
as  much  as  possible,  and,  further,  that  two  similar 
tubes  repelled  each  other,  he  was  able  to  give 
a  clear  explanation  of  the  various  electrical  pheno- 
mena. Thus  the  attraction  between  two  oppositely 
charged  bodies  was  the  result  of  the  tendency 
of  the  tubes  connecting  them  to  contract  ;  the 


?a  MOLECULAR  PHYSICS 

repulsion  between  two  like  charges  was  due  to 
the  mutual  repulsion  between  the  tubes  of  force 
radiating  from  each  of  them.  An  electric  current 
was  the  motion  of  one  of  the  ends  of  the  tubes  of 
force  along  the  conductor,  while  the  magnetic  effect 
in  the  neighbourhood  of  the  current  was  due  to 


FIG.  16. — DISTRIBUTION  OF  TUBES  OF  ELECTRIC  FORCE  ROUND 
AN  ELECTRON  AT  REST. 

the   motion   of   the    tubes    of    force    through    the 
surrounding  medium. 

The  concentration  of  attention  upon  the  pheno- 
mena of  currents  which  marked  the  latter  half  of  last 
century  tended  to  throw  somewhat  into  oblivion  this 
conception  of  Faraday.  The  recent  researches  with 
which  we  are  dealing  have,  however,  found  in  it  a 
most  powerful  weapon,  and  are  tending  to  give  to 
these  tubes  of  force  a  definite  significance  and  con- 


NATURE   AND   SIZE   OF  AN   ELECTRON    73 

Crete  existence  of  which  even  their  originator  per- 
haps hardly  dreamed. 

Let  us  add  to  the  postulates  already  made  by 
Faraday  this  additional  assumption,  that  a  tube  of 
force  when  moving  through  the  ether  is  able  to  grip 
a  certain  quantity  of  that  subtle  fluid,  in  much  the 
same  way  that  a  cylinder  carries  along  with  it  a 
definite  mass  of  any  liquid  through  which  it  moves. 
For  a  single  charged  particle  at  a  considerable  dis- 
tance from  any  other  attracting  bodies  the  lines  of 
force  will  radiate  out  in  straight  lines  from  its  surface, 
and,  if  the  latter  is  spherical,  the  tubes  will  space 
themselves  evenly  around  it  owing  to  their  mutual 
repulsion.  In  section,  therefore,  they  will  appear 
somewhat  as  in  Fig.  16. 

Suppose  this  system  to  be  moving  through  space 
in  the  direction  OA  with  a  velocity  v.  If  our 
analogy  with  the  case  of  a  body  moving  through 
water  holds,  the  tubes,  like  OB,  which  move  at  right 
angles  to  their  length,  will  grip  the  maximum  amount 
of  the  ether  through  which  they  are  moving,  while 
tubes  like  OA,  which  are  moving  along  their  length, 
will  carry  none.  It  will  thus  be  seen  that  the  dis- 
tribution of  energy  in  the  field  surrounding  the  par- 
ticle will  correspond  exactly  with  the  distribution  of 
energy  in  the  electro-magnetic  field  of  which  it  is 
supposed  to  be  a  visualisation.  The  electrical  mass 
of  the  particle  will  then  be  the  whole  mass  of  the 
ether  gripped  by  these  radiating  tubes. 

Now  it  is  a  well-known  fact  that  a  cylinder 
moving  through  a  fluid  in  the  direction  of  its  own 
length  is  not  in  stable  equilibrium.  In  accordance 
with  the  well-known  principle  of  least  action,  the 
cylinder  will  tend  to  turn  so  as  to  offer  the  greatest 
possible  resistance  to  the  motion,  that  is  to  say,  it 
will  tend  to  set  itself  at  right  angles  to  the  direction 
in  which  it  is  being  compelled  to  move.  If  this 
holds  for  tubes  of  force  travelling  through  the  ether, 


74 


MOLECULAR   PHYSICS 


then  tubes  like  OA  are  not  in  stable  equilibrium,  but 
will  tend  to  turn  into  the  plane  of  OB,  which  we  may 
call  the  equatorial  plane.  It  can  be  shown  from  the 
principles  of  electricity  that  such  a  tendency  does 
indeed  exist.  The  repulsion  between  the  different 
tubes  will,  of  course,  tend  to  keep  OA  in  position, 
and,  as  this  repulsion  is  very  great,  at  moderate 


pIG 


—  DISTRIBUTION  OF  TUBES  OF  ELECTRIC  FORCE  ROUND 
A  MOVING  ELECTRON. 


velocities  the  effect  we  are  considering  will  be  quite 
negligible.  The  force,  however,  tending  to  displace 
the  tubes  increases  with  the  velocity  of  the  particle, 
so  that  at  speeds  approaching  that  of  light  there  is 
a  very  perceptible  shifting  of  the  lines  of  force  into 
the  equatorial  plane,  as  indicated  in  Fig.  17.  But 
we  have  noted  that  the  mass  of  ether  gripped  by  the 


NATURE   AND   SIZE   OF  AN   ELECTRON    75 

tubes  in  this  position  is  greater  than  that  which  they 
originally  held.  Thus  we  arrive  at  the  somewhat 
startling  result  that  the  electrical  mass  of  a  particle 
is  not  a  constant,  but  depends,  at  any  rate  at  high 
velocities,  upon  the  speed  with  which  it  is  moving. 

We  have  followed  out  the  theory  of  the  variation 
of  electrical  mass  from  the  standpoint  of  Faraday's 
tubes  of  force,  because  in  the  first  place  it  gives  us 
at  once  a  clear  and  vivid  picture  of  the  processes 
which  are  going  on  in  the  field,  while  in  the  second 
place  we  are  being  gradually  driven  to  the  con- 
clusion that  some  such  entities  do  play  a  very 
important  part  in  the  phenomena  of  the  electric 
field.  The  fact  of  the  variation  of  electric  mass  with 
the  speed,  however,  does  not  depend  in  the  least 
upon  the  particular  way  in  which  we  choose  to 
regard  the  electric  field,  but  is  a  direct  though  obscure 
consequence  of  the  fundamental  facts  of  the  science. 

The  exact  relation  between  the  electrical  mass  of 
a  moving  charge  and  its  velocity  depends  somewhat 
on  the  assumptions  we  make  as  to  the  distribution 
and  geometrical  configuration  of  the  charge.  Thus, 
starting  from  different  ideas  of  the  shape  of  the 
electron  and  the  way  in  which  its  charge  is  arranged, 
different  mathematicians  have  arrived  at  somewhat 
different  formulae  for  this  relation.  Fortunately, 
when  these  are  reduced  to  figures  the  differences 
between  the  best  of  them  are  so  small  that  our 
experiments  are  scarcely  accurate  enough  to  settle 
definitely  between  them.  One  of  the  most  success- 
ful is  that  of  Dr.  Abraham,  who  deduces  that 

electrical  mass  ;;/  at  a  velocity  v          3    (\  +  fl2  .       i  -h  0         \ 
electrical  mass  m0  f  or  small  velocities  "4 )82  \  "  2/8         &  i  -  £         /' 

where  /3  is  the  ratio  of  the  velocity  of  the  particle 
to  the  velocity  of  light. 

Let  us  see  now  how  these  results  assist  us  to 
discover  the  nature  of  an  electron.  The  total  mass 


76  MOLECULAR   PHYSICS 

of  the  electron  may  be  made  up  of  two  parts  :  its 
mechanical  mass,  which  is  constant  and  independent 
of  the  velocity,  with  which  the  electron  is  moving  ; 
and  an  electrical  mass,  which  increases  with  the 
velocity  in  the  way  we  have  just  considered.  If  the 
electrical  mass  of  the  electron  is  small  compared 
with  its  ordinary  mechanical  mass,  then  there  will  be 
very  little  variation  in  the  total  mass  of  the  electron 
as  the  speed  is  increased.  If,  on  the  other  hand,  the 
whole  of  the  mass  is  electrical  in  its  nature,  the  total 
mass  of  the  electron  should  increase  at  the  rate  given 
by  the  formula  of  Abraham.  If  part  of  the  mass  is 
mechanical  and  part  electrical,  the  rate  of  increase 
of  the  whole  mass  of  the  electron  with  increasing 
velocity  will  be  somewhere  between  these  two 
values. 

If  we  substitute  numerical  values  in  the  equation 
given  above,  it  will  be  found  that  the  difference 
between  m  and  m0  is  quite  inappreciable  unless  the 
speed  of  the  particle  is  very  high  indeed.  Thus 
when  the  velocity  is  as  much  as  one-tenth  that  of 
light,  the  increase  in  the  electrical  mass  only  amounts 
to  about  i%,  while  even  when  the  velocity  reaches 
one-third  that  of  light,  that  is  to  say,  over  60,000 
miles  per  second,  the  increase  in  the  mass  is  only 
about  5%.  As  this  is  the  maximum  velocity 
attainable  in  a  discharge  tube  it  might  have  been 
thought  that  the  experimental  investigation  of  the 
variation  of  mass  with  speed  lay  forever  beyond  our 
reach. 

Fortunately  this  is  not  the  case.  Experiments 
have  shown  that  the  /3-particles  from  radium,  while 
otherwise  similar  to  cathode  rays,  travel  with 
velocities  enormously  greater  even  than  those  of  the 
particles  in  a  discharge  tube,  in  some  cases  approach- 
ing within  4%  of  the  velocity  of  light  itself.  For 
speeds  such  as  this  the  electrical  mass  should  be 
nearly  three  times  its  ordinary  value,  and  thus,  by 


NATURE  AND   SIZE   OF  AN   ELECTRON    77 


4   cms. 

FIG   18. — KAUFMANN'S  APPARATUS  FOR  DETERMINING  THE 
MASS  OF  A  /3-PARTICLE. 

careful  experiments  on  these  particles,  we  might 
well  hope  to  put  to  the  test  the  theories  we  have 
propounded. 

Such  experiments  have  been  made  with  exquisite 


78  MOLECULAR   PHYSICS 

skill    and    care    by    Kaufmann.     In    principle    the 
methods   he   employed   were   identical   with   those 


Y 


0 


FIG.  19. — KAUFMANN'S  EXPERIMENTAL  CURVE  FOR  THE 
ELECTRIC  MAGNETIC  DEFLEXION  OF  THE  /8  RAYS  FROM 
RADIUM. 

already  -described.  The  /3-particles  given  out  by 
a  small  quantity  of  radium  placed  at  R  (Fig.  18), 
passed  through  a  fine  hole  in  a  lead  screen  at  A, 
before  finally  falling  on  a  photographic  plate  at  P. 


NATURE   AND   SIZE   OF   AN    ELECTRON    79 

Before  reaching  the  hole  at  A  the  particles  passed 
between  two  parallel  plates,  which  could  be  very 
carefully  adjusted  by  means  of  a  series  of  levelling 
screws,  and  which  were  charged  to  a  high  difference 
of  potential.  The  whole  of  the  apparatus  was  placed 
between  the  poles  of  a  strong  electromagnet  N,  S, 
arranged  so  that  the  electric  and  magnetic  fields  were 
parallel  to  each  other  and  therefore  the  correspond- 
ing deflections  they  produced  at  right  angles  to  each 
other,  exactly  as  in  Professor  Sir  J.  J.  Thomson's 
experiments  on  the  positive  rays.  Apart  from  the 
differences  in  velocity  all  the  /3-particles  are  identical. 
Thus,  for  every  value  of  the  velocity  v  there  is  only 
one  corresponding  value  for  the  mass  m.  Hence 
the  beam  of  rays  is  drawn  out  on  the  plate  into 
a  single  curve  (Fig.  19),  every  point  on  which  corre- 
sponds to  particles  with  a  particular  mass  and  speed. 

This  curve  can  be  measured  up  with  a  micrometer 
in  exactly  the  same  way  as  has  been  described  for 
the  positive  ray  curves,  and  the  mass  and  speed  of 
the  particles  deduced  by  equations  (c)  and  (d) 
(Chapter  IV.).  The  values  of  the  constants  ki  and 
£2  for  the  apparatus  were  very  accurately  deter- 
mined, as  were  also  the  strengths  of  the  electric  and 
magnetic  fields.  In  this  way  Kaufmann  obtained 
results  which  he  regarded  as  being  accurate  to 
within  i*5%,  a  very  notable  achievement. 

Some  of  the  results  obtained  are  given  in  Table  V. 
The  first  column  of  the  table  gives  the  velocity  of 
the  particles,  the  second  the  value  of  ft  in  Abraham's 
formula,  that  is  to  say,  the  ratio  of  the  velocity 
of  the  particle  to  the  velocity  of  light.  In  the 
third  column  we  have  Kaufmann's  experimental 
values  for  the  ratio  of  the  whole  mass  of  the  particles 
to  their  mass  at  small  velocities.  The  last  column 
gives  the  theoretical  value  of  this  ratio,  deduced 
from  Abraham's  equation,  on  the  assumption  that 
the  whole  of  the  mass  is  electrical. 


8o 


MOLECULAR   PHYSICS 


It  will  be  seen  how  very  closely,  all  things 
considered,  the  two  sets  of  figures  agree.  The 
experimental  values  for  the  ratio  m/mti  increase, 
if  anything,  even  more  rapidly  than  theoretical. 
This  would  imply  that,  if  anything,  the  mechanical 
mass  of  the  electron  is  negative,  which  is,  of  course, 
an  impossibility.  The  small  discrepancy  between 
the  two  sets  of  figures  is  no  doubt  due  to  a  lack  of 


TABLE   V. 

Kaufmann's  values  for  the  variation  of  the  mass  of  a 
/3-particle  with  change  of  velocity. 


Velocity  of  the  j3-particle. 

0  - 

•of  particle 

bp 
O 

Experimental 
value  of 
ntlm0  for  the 

/«////    for 
Abraham's 

1 

velocit 

j3-particle. 

equation. 

2-88  x  io10  cm.  per  sec. 

•9<: 

>3 

2-70 

2-52 

2-85 

•9z 

19 

2*24 

2-80 

'9: 

13 

2*09 

2*I4 

2-65 

•8^ 

>3 

I  '96 

1-81 

2*49 

•8- 

*o 

I  "70 

1-61 

2-41 

•8c 

)i 

1-61 

1*54 

2'20 

•7: 

*2 

1-41 

1-41 

knowledge  as  to  the  exact  nature  of  the  distribution 
of  the  electronic  charge. 

We  have  now  discussed  the  evidence  for  our 
original  statement  that  the  whole  mass  of  the 
electron  is  electrical  in  origin  and  due  entirely  to 
the  charge  it  carries.  Granting  this  conclusion, 
we  can  at  once  determine  the  dimensions  of  the 
electron,  and  so  complete  our  knowledge  of  its 
properties. 


NATURE   AND   SIZE   OF   AN   ELECTRON    81 
We  have  seen  that  the  electrical  mass  of  a  charge 

2  P 

e  for  moderate  speeds  is  equal  to  -   -  where  a  is  the 

3  * 

radius  of  the  space  occupied  by  the  charge.  The 
mass  of  an  electron  is  8*8  X  io~28  gms.,  while  the 
value  of  the  charge  it  carries  is  1*57  X  io~20  units. 
Substituting  these  values  in  the  formula  we  find  that 
the  radius  of  an  electron  is  1*87  X  io~13  cms. 

We  have  stated  elsewhere  that  the  radius  of  an 
atom  is  of  the  order  of  io~8  cms.,  and  have  attempted 
to  form  some  idea  of  the  exceeding  smallness  of 
this  magnitude.  We  may  now  say  that  small  as 
the  atom  is,  the  electron  is  so  much  smaller  that 
the  electron  bears  to  the  atom  which  contains  it 
very  much  the  same  relation  as  a  pea  to  a 
cathedral. 

We  have  seen  that  the  whole  of  the  mass  of  the 
electron  is  due  to  the  charge  which  it  carries.  The 
thought  at  once  suggests  itself  :  Are  there  indeed 
two  kinds  of  mass  or  is  all  mass  electrical  in  its 
origin  ?  Probably  most  physicists  cherish  this 
belief  at  the  bottom  of  their  hearts,  but  it  cannot 
at  present  be  said  to  be  much  more  than  a  pious 
hope.  The  mass  of  a  negative  electron  is  about 
TTOO  Part  °f  the  mass  of  a  hydrogen  atom. 
Neglecting  the  positive  charge  of  the  atom,  of  which 
we  know  practically  nothing,  it  would  require 
1,700  electrons  to  make  up  the  mass  of  a  single 
hydrogen  atom.  This  of  course  is  not  a  priori  an 
impossible  number  considering  the  smallness  of 
the  electron  ;  and  speculations  along  these  lines 
were  for  a  time  freely  indulged  in.  In  this  case, 
however,  experiment  failed  to  confirm  the  bold 
conjecture.  The  number  of  electrons  in  the  atom 
has  been  determined  at  any  rate  approximately, 
and  affords  no  support  for  such  a  theory. 

As  this  number  is  one  of  considerable  theoretical 
importance,  we  may  perhaps  be  allowed  to  describe, 
M.P.  6 


82  MOLECULAR   PHYSICS 

very  briefly,  one  of  the  methods  by  which  attempts 
have  been  made  to  determine  it.  Consider  a 
single  electron  flying  through  a  sheet  of  metal.  With 
the  huge  velocity  which  it  possesses  a  sheet  of 
aluminium,  say  Jth  mm.  thick,  is  not  a  very  serious 
obstacle  to  a  /3-particle.  Neglecting  for  a  moment 
the  positive  charge  which  keeps  the  atom  together, 
the  various  atoms  which  our  particle  encounters 
must  present  to  the  particle  the  appearance  of  a 
series  of  large  chambers,  empty  save  for  a  certain 
number  of  particles,  minute  in  comparison  with 
the  atom,  and  similar  to  itself. 

At  a  considerable  distance  these  fixed  electrons 
will  have  little  effect  on  the  moving  corpuscle.  If, 
however,  in  its  flight  it  approaches  one  of  them 
closely  it  will  be  repelled,  as  the  two  particles  each 
carry  a  negative  charge.  The  nearer  it  approaches 
the  greater  will  be  the  repulsion,  and  the  further  the 
moving  particle  will  be  deflected  from  its  original 
path.  We  may  call  this  a  collision.  It  is,  in  fact 
the  same  sort  of  collision  as  we  imagine  to  take  place 
between  two  gas  molecules.  The  direction  in  which 
the  particle  will  be  deflected  will  be  perfectly  arbi- 
trary, and  a  second  collision  may  actually  undo  the 
work  of  the  -first.  On  the  whole,  however,  the 
greater  the  number  of  collisions  the  greater  will  be 
the  deflection,  and  it  is  not  beyond  the  possibilities 
of  mathematics  to  determine  the  most  probable 
effect  of  a  given  number  of  these  deflections.  The 
problem  is  indeed  mathematically  equivalent  to  the 
well-known  theorem  of  the  drunkard's  walk.  Sup- 
pose a  drunkard  walks  so  many  yards  before  falling 
down,  and  after  each  fall,  having  lost  all  sense  of 
locality,  sets  out  again  in  some  new  and  arbitrary 
direction,  at  what  distance  from  his  starting  point 
will  he  be  most  likely  to  be  found  after  a  given 
number  of  falls  ?  This  problem,  under  a  somewhat 
different  title,  has  been  solved  by  Lord  Rayleigh 


NATURE   AND   SIZE   OF   AN   ELECTRON    83 

in  that  marvellous  compendium  of  mathematical 
physics,  the  "Theory  of  Sound/' 

If  then  we  can  find  experimentally  the  most 
probable  deflection  of  a  /3-particle  after  passing 
through  a  certain  thickness  of  solid  matter,  we  can 
deduce  the  number  of  collisions  it  has  made  in  its 
passage  through  the  solid,  and  hence  the  number  of 
electrons  in  unit  volume  of  the  substance.  Since 
the  number  of  atoms  per  cubic  centimetre  of  any 
substance  can  readily  be  deduced  from  the  data 
given  in  Chapter  III.,  the  number  of  electrons  in 
each  atom  can  at  once  be  determined. 

A  series  of  experiments  upon  these  lines  was 
recently  performed  by  the  author.  By  various 
experimental  devices,  which  it  would  take  us  too  far 
from  our  course  to  describe,  the  mean  angle  through 
which  an  originally  parallel  pencil  of  /3-rays  was 
scattered  in  passing  through  sheets  of  various  sub- 
stances was  determined.  By  experimenting  on 
sheets  of  different  thicknesses  the  author  was  able 
to  show  that  the  mathematical  treatment  outlined 
above  was  applicable  to  this  particular  case,  and 
hence  to  deduce  the  number  of  electrons  in  the 
atoms  of  the  various  elements  experimented  upon. 

The  matter  is,  perhaps,  hardly  so  simple  as  we 
have  described  it.  We  have  neglected  so  far  the 
effect  of  the  positive  electrification  which  we  know 
must  be  present  in  the  atom  if  the  latter  is  to  be 
electrically  neutral.  This  will  exert  a  certain 
attraction  on  the  flying  electrons. 

Unfortunately,  we  are  not  yet  acquainted  with 
the  nature  of  positive  electricity.  Professor  Sir 
J.  J.  Thomson's  experiments  on  the  positive  rays, 
brilliant  as  they  have  been,  have  not  at  present 
thrown  much  light  upon  this  exceedingly  difficult 
problem.  For  the  present  the  term  "positive  elec- 
trification "  remains  for  the  physicist  very  much 
what  the  term  "  catalytic  action  "  is  for  the  chemist 

6—2 


84  MOLECULAR  PHYSICS 

—a  not  too  humiliating  method  of  confessing 
ignorance.  If  we  suppose  that  the  positive  electri- 
city is  distributed  uniformly  over  a  sphere  the  size 
of  the  atom  (a  hypothesis  which  lends  itself  very 
readily  to  mathematical  treatment),  the  author's 
result  would  indicate  that  the  number  of  electrons 
in  an  atom  is  almost  exactly  three  times  its  atomic 
weight.  That  is  to  say,  the  number  of  electrons 
in  a  hydrogen  atom  would  be  three.  If  we  go  to 
the  other,  extreme,  and  suppose  that  the  positive 
electrification  is  a  sort  of  nucleus  at  the  centre  of  the 
atom,  and  that  the  electrons  revolve  round  it  some- 
what after  the  manner  of  the  rings  of  Saturn,  the 
number  of  electrons  in  a  hydrogen  atom  works  out 
at  unity,  the  number  in  any  other  atom  being  equal 
to  its  atomic  weight.  The  assigning  of  unit  atomic 
weight  to  hydrogen  would  then  have  a  very  definite 
physical  significance,  as  it  would  be  the  lightest 
atom  which  could  possibly  exist.  In  either  case 
the  number  of  electrons  in  an  atom  is  only  a  very 
small  multiple  of  its  atomic  weight.  We  cannot, 
therefore,  assign  any  appreciable  fraction  of  the  mass 
of  the  atoms  to  the  negative  electrons  it  contains. 

There  still  remains,  of  course,  the  possibility  that 
the  mass  is  electrical,  but  that  it  resides  in  the 
positive  portion  of  the  atom.  If  the  formula  for  the 
electric  mass  be  examined,  it  will  be  seen  that  for  a 
given  charge  the  mass  is  inversely  proportional  to 
the  radius  of  the  sphere  upon  which  it  is  concentrated. 
If  we  suppose  that  the  positive  charge  on  the 
hydrogen  atom  to  be  concentrated  upon  a  sphere 
only  xt'oo  °f  the  size  of  the  negative  electron,  its 
mass  would  be  1,700  times  as  great,  that  is  to  say, 
equal  to  that  of  the  hydrogen  atom.  Our  perfect 
ignorance  of  the  nature  of  positive  electricity  renders 
the  suggestion  not  untenable,  though  evidence  for  it 
is  sadly  lacking.  For  the  present  our  belief  in  the 
electro-magnetic  nature  of  all  mass  remains  an 


NATURE   AND   SIZE   OF  AN   ELECTRON    85 

expression  of  our  faith  that  all  the  varied  phe- 
nomena with  which  we  have  to  deal  are  manifesta- 
tions of  some  single  principle  or  essence  which 
underlies  them  all.  To  what  extent  future  experi- 
ment will  realise  our  belief  in  the  present  instance 
remains  to  be  seen. 


CHAPTER   VI. 
THE  CHEMISTRY  OF  THE  MODEL  ATOM. 

WE  have  now  learned  all  that  is  to  be  known 
about  electrons,  their  nature,  their  mass,  their 
charge,  and  their  dimensions.  We  have  seen  that 
they  form  a  part  of  all  atoms,  and  have  discovered, 
at  any  rate  approximately,  how  many  of  them  we 
may  expect  to  find  in  an  atom  of  any  given  element. 
We  have  seen  also  that  electrons  form  a  very  minute 
part  of  the  mass,  and  a  still  smaller  part  by  volume 
of  the  whole  atom. 

It  might  be  thought  therefore  that  their  influence 
in  determining  the  properties  of  the  atom  would  be 
proportionately  small.  There  is  much  evidence 
however  that  this  is  not  the  case,  as  we  shall  have 
occasion  to  see  during  our  further  survey  of  molecular 
physics.  The  electrons  are  small  but  they  are 
fmobile.  It  is  entirely  owing  to  this  mobility  that 
we  are  so  well  acquainted  with  their  properties. 
It  is  owing  to  this  same  mobility  that  they  exercise 
such  a  marked  influence  upon  the  chemical  and 
physical  character  of  the  atom. 

Our  difficulties  in  constructing  a  satisfactory 
model  of  an  atom  lie,  as  we  have  already  seen,  in 
our  almost  complete  ignorance  of  the  nature  of  the 
residue  of  an  atom  from  which  the  electrons  have 
been  extracted.  The  atom  can  lose  at  any  rate 
|  some  of  its  electrons  without  any  serious  change  of 
properties,  and  as  the  normal  atom  is  neutral,  the 
residues  aiter  extracting  the  electrons  must  possess 


CHEMISTRY   OF   THE   MODEL   ATOM       87 

positive  electrification.     Beyond  this  we  know  little  , 
or  nothing. 

Three  views  are  possible.  In  the  first  place  we 
may  assume  of  our  residues  what  the  earlier  atomists 
assumed  of  their  atoms,  that  they  are  fundamentally 
different  in  character,  that  copper  is  copper,  and 
tin  is  tin,  and  that  there  is  no  more  to  be  said  about 
it.  This  would  be  to  abandon  all  hope  of  attaining 
any  explanation  of  those  recurring  similarities 
between  the  properties  of  the  different  elements 
which  are  so  clearly  brought  out  in  that  greatest 
of  the  generalisations  of  descriptive  chemistry,  the 
periodic  classification  of  the  elements.  This  is  a 
policy  of  despair. 

Assuming,  then,  that  the  remainder  of  all  the"1 
atoms  is  composed  of  different  amounts  of  the  same 
stuff,  call  it  matter  or  positive  electrification  as 
we  will,  this  substance  may  be  either  continuous 
or  divided  up  into  larger  or  smaller  particles.  The 
fact  that  the  a-particles  given  out  by  all  radio- 
active substances  are  identical  might  suggest  that 
these  particles  are  the  stones  from  which  the  edifice 
of  the  atom  is  built  up.  The  a-particle  is,  however, 
too  complex  a  structure  to  serve  as  a  protyle  ;  it 
is,  for  example,  four  times  as  heavy  as  our  lightest 
atom,  and,  in  all  probability  contains  at  least  two 
electrons.  Professor  Nicholson  has  built  up  an 
interesting  chemical  system  from  protyle  atoms  of 
atomic  weight,  i,  2,  3,  and  4,  but  these  in  themselves 
would  in  all  probability  be  complicated  structures, 
and  in  the  absence  of  further  evidence  on  which  to 
work  it  seems  better  to  proceed  at  once  to  thej 
fundamentals. 

The  existence  of  a  positive  electron  is  not  quite^ 
beyond  the  realms  of  possibility.    It  may  be  that 
there  is  some  sort  of  undetected  one-sidedness  about 
our  experiments  which  accounts  for  our  complete 
failure  to  observe  it.     If  at  any  time  it  makes  its 


88  MOLECULAR  PHYSICS 

appearance,  it  is  possible  that  something  of  the 
argument  which  follows  may  have  to  be  referred  to 
the  positive  rather  than  to  the  negative  electron. 

Taking  all  the  facts  into  consideration,  the  most 
probable  hypothesis  at  the  present  moment  is  the 
one  which  regards  the  positive  part  of  the  atom  as 
forming  either  a  uniform  sphere,  coterminous  with 
the  atom,  or  a  dense  nucleus  at  its  centre.  In  the 
first  hypothesis  the  electrons  would  move  about 
within  the-  positive  sphere  and  would  be  attracted 
with  a  force  varying  directly  as  their  distance 
from  the  centre  of  the  sphere.  On  the  second 
hypothesis  some,  at  any  rate,  of  the  electrons  would 
be  outside  the  positive  charge  and  revolve  as 
satellites  around  it,  like  the  rings  round  the  planet 
Saturn,  being  attracted  to  it  in  this  case  with  a 
force  varying  inversely  as  the  square  of  the  distance. 

The  latter  suggestion  has  very  much  to  recommend 
it,  but  it  has  also  the  very  great  defect  from  our 
immediate  point  of  view  that  it  does  not  lend  itself 
at  all  readily  to  mathematical  treatment.  In  other 
words  we  cannot  easily  determine  from  the  laws 
governing  such  a  system  the  way  in  which  the 
electrons  would  be  arranged,  and  hence  we  cannot 
easily  deduce  the  properties  to  be  expected  in  such 
an  atom.  It  is  most  probable  that  the  arrangement 
of  the  electrons  in  the  two  cases  would  exhibit  the 
same  general  features,  though,  of  course,  the  actual 
values  in  any  given  case  would  be  different.  As  it 
is  not  at  all  likely  that  either  of  these  simple 
systems  will  eventually  be  found  adequate  to 
represent  the  atom  of  any  real  substance,  we  may, 
without  any  loss  of  generality,  confine  our  attention 
;  to  the  simpler  case. 

The  grouping  of  a  number  of  electrons  in  a 
sphere  of  positive  electrification  which  is  just 
sufficient  to  neutralise  their  charges  at  points 
outside  the  sphere,  has  been  investigated  theoreti- 


CHEMISTRY   OF  THE   MODEL  ATOM       89 

cally  by  Professor  Sir  J.  J.  Thomson.  A  single 
electron  if  at  rest  will  place  itself  at  the  centre  of 
the  sphere,  or  if  in  motion  will  describe  a  circle 
around  that  point  with  a  radius  depending  on  its 
velocity.  Two  electrons  would  occupy  the  opposite 
ends  of  the  diameter  of  a  circle  whose  radius  is 
equal  to  half  the  radius  of  the  positive  sphere  while 
three  electrons  would  arrange  themselves  at  the 
points  of  an  equilateral  triangle.  The  arrangement 
of  four  electrons  at  the  corners  of  a  square  is,  however, 
not  a  stable  grouping  if  the  ring  of  electrons  is  at 
rest,  but  becomes  possible  if  they  are  revolving 
round  the  centre  with  a  speed  which  exceeds  a 
certain  critical  value.  If  their  velocity  falls  below 
this  the  system  collapses  into  a  tetrahedron  with  an 
evolution  of  energy. 

The  determination  of  the  arrangement  of  any 
number  of  electrons  in  a  space  of  three  dimensions 
becomes  at  first  difficult  and  finally  impossible. 
A  few  cases  have,  however,  been  worked  out.  Thus 
six  electrons  would  arrange  themselves  at  the 
corners  of  a  regular  octahedron,  but,  on  the  other 
hand,  the  arrangement  of  eight  at  the  corners  of  a 
cube  is  not  stable  and  will  collapse  into  two  tetra- 
hedra,  one  inside  the  other,  unless  we  station  at  least 
one  other  electron  within  it.  We  are  thus  brought 
face  to  face  with  one  of  the  most  important  generali- 
sations in  electron  grouping,  namely,  that  it  is  quite 
impossible  for  any  system  to  make  a  large  display 
of  electrons  near  its  surface  without  a  corresponding 
stock  within.  The  presence  of  a  given  number  of 
electrons  near  the  outside  of  the  atom  demands 
that  there  shall  be  a  certain  definite  number  of 
electrons  within  in  order  that  the  system  may  be 
stable.  To  use  a  commercial  metaphor,  an  atom 
cannot  have  all  its  goods  in  the  shop  window. 
Otherwise  there  will  be  inevitable  collapse  into  some 
less  pretentious  system. 


MOLECULAR   PHYSICS 


The  analysis  becomes  simpler,  and  leads  to  the 
same  general  results,  if  we  consider  the  electrons  as 
confined  to  a  single  plane  instead  of  being  able  to 
move  in  three  dimensional  space,  a  supposition 
which  is  not  altogether  without  justification  on 
experimental  grounds.  This  case  has  the  further 


1 


FIG.  20. — A  "MODEL"  ATOM. 

advantage  that  it  can  be  studied  experimentally  in 
a  variety  of  ways.  Of  these  the  very  beautiful  experi- 
ments of  Mayer,  though  designed  for  quite  other 
purposes,  are  perhaps  the  simplest  to  reproduce. 

A  large  number  of  needles  are  magnetised 
together  in  a  solenoid,  and  are  floated  vertically  in 
a  basin  of  water  by  pushing  all  their  (say)  north 


CHEMISTRY   OF  THE   MODEL  ATOM        91 

poles  into  small  corks,  their  south  poles  being  at 
the  same  depth  below  the  water.  These  latter  repel 
each  other,  just  as  do  the  electrons,  according  to  an 
inverse  square  law.  To  represent  the  action  of  the 
positive  sphere  we  may  place  a  strong  electro-magnet 
beneath  the  bowl  with  its  north  pole  upwards. 
It  can  be  shown  that  the  attraction  of  this  magnet 
for  the  tiny  south  poles  is  (for  the  horizontal  plane 
in  which  alone  they  are  able  to  move)  approxi- 
mately proportional  to  their  distance  from  a  point 
immediately  above  the  pole.  Fig.  20  is  a  photo- 
graph showing  ten  of  these  small  magnets.  It  will 
be  seen  that  they  are  arranged  in  two  rings  of  seven 
and  three  respectively.  The  attracting  electro- 
magnet is  concealed  below  the  board. 

On  making  the  experiment  it  is  found  that  the 
greatest  number  of  magnets  which  we  can  have  in 
an  empty  ring  is  five.  If  a  sixth  is  added  the 
ring  breaks  up,  the  magnets  gradually  settling  down 
into  an  arrangement  of  five  on  the  outside  with  one 
in  the  middle.  The  number  which  must  be  placed 
in  the  middle  rapidly  increases  with  the  number  in 
the  outer  ring.  Thus  an  outer  ring  of  twelve 
requires  at  least  eight  inside,  and  one  of  thirty  no 
less  than  one  hundred  and  one  for  stability  to  be 
possible.  As  these  inner  magnets  are  subject  to 
exactly  the  same  laws  as  the  outer  ones,  the  whole 
system,  whether  of  magnets  or  electrons,  splits  up 
into  a  series  of  concentric  rings,  with  a  perfectly 
definite  number  of  particles  in  each. 

A  complete  mathematical  solution  has  been 
obtained  by  Professor  Thomson.  Table  VI.  con- 
tains his  results  foi  the  model  atoms  in  which  the 
number  of  electrons  is  not  more  than  fifty-two.  I 
would  point  out  very  emphatically  at  this  point 
that  no  stress  must  be  laid  on  the  exact  numbers 
given  in  this  Table.  The  simplifications  we  have 
made  are  too  many  to  render  it  even  possible  that 


92  MOLECULAR   PHYSICS 

these  arrangements  represent  actual  atoms  of  any 
real  substance.  Neither  does  the  weight  of  the 
argument  rest  on  any  numerical  relations  between 
the  numbers  of  electrons  in  the  different  rings.  The 
general  law  of  electron  grouping  enunciated  above 
when  discussing  three  dimensional  systems  is  amply 
sufficient  for  all  that  follows,  and  is  all  we  have  at 
present  any  right  to  make.  It  is,  however,  of  the 
greatest  assistance  in  following  the  arguments  to 
clothe  our  abstract  principles  in  concrete  form  and 
to  consider  some  definite  case  where  the  relationships 
can  be  expressed  in  numerical  form.  The  system 
chosen  is  the  simplest  for  the  purpose. 

The  first  row  in  Table  VI.  contains,  with  these 
limitations,  the  "  atoms  "  for  which  there  is  only 
one  ring  of  electrons,  the  second  those  with  two, 
and  so  on,  the  upper  number  being  in  each  case  that 
contained  in  the  outer  ring.  Thus  n,  5,  i,  which 
commences  series  C,  implies  that  this  atom  contains 
an  outermost  ring  of  eleven  electrons  with  an  inner 
ring  of  five  and  a  single  electron  at  the  centre. 
Remembering  that  the  number  of  electrons  in  the 
atom  is  proportional  to  the  atomic  weight,  it  will  be 
seen  that  this  Table  represents  a  series  of  model 
elements  arranged  according  to  their  ascending 
atomic  weight. 

A  very  cursory  glance  at  this  Table  at  once 
reveals  a  very  striking  similarity  to  Mendeleef's 
periodic  classification  of  the  elements.  Thus,  for 
example,  if  we  assign  any  chemical  or  physical 
property  to  the  existence  in  the  atom  of  an  arrange- 
ment of  electrons  such  as  (5,  i)  this  property  will 
disappear  as  we  pass  along  the  series  to  atoms  with 
different  groupings,  and  consequently  different 
properties.  Proceeding  still  further,  however,  we 
come  to  a  place  where  the  original  grouping  (5,  i)  is 
restored  with  the  addition  of  an  extra  outer  ring  of 
eleven  electrons  (n,  5,  i).  ••'-••  3 


CHEMISTRY   OF   THE   MODEL   ATOM       93 

This  grouping  again  disappears  as  we  pass  along 
series  C,  to  reappear  again  with  an  extra  ring  of 
fifteen  at  the  beginning  of  series  D,  and  with  a 
further  ring  of  seventeen  in  series  E. 

Thus  any  property  associated  with  a  given 
grouping  of  electrons  will  recur  again  and  again  at 
intervals,  as  the  number  of  electrons  in  the  model 
atom  is  increased.  It  can  hardly  be  necessary  to 
point  out  how  closely  this  resembles  the  arrangement 
of  the  elements  according  to  atomic  weight  where 
the  properties  of  the  element  sodium,  for  example, 
disappear  as  we  proceed  to  elements  of  higher 
atomic  weight,  only  to  make  their  appearance  again 
with  slight  modifications  when  we  arrive  at  the 
element  potassium. 

There  are  many  other  resemblances  which  may 
be  pointed  out  between  the  periodic  Table  and  our 
scheme  of  electrons.  In  the  first  place  it  will  be 
seen  that  in  the  same  group  the  atoms  of  series  D  and 
E  have  four  rings  in  common  with  each  other, 
while  those  in  series  B  and  C  have  only  two.  The 
elements  of  higher  atomic  weight  will  resemble  each 
other  more  closely  than  the  elements  of  lower 
atomic  weight.  This  again  is  a  commonplace  of 
the  periodic  classification.  Further,  it  will  be  seen 
that  at  certain  places  in  the  Table  the  groupings  are 
in  rapid  change,  while  at  others  the  configuration 
alters  much  more  slowly.  This  again  corresponds 
very  closely  with  what  actually  occurs  in  the 
arrangement  of  the  elements  where  starting,  for 
example,  at  sodium,  the  alkaline  properties  gradually 
disappear  as  we  pass  through  magnesium  and 
aluminium,  to  be  replaced  by  acid  ones  at  sulphur 
and  chlorine.  As  we  proceed  further,  however,  there 
is  a  sudden  recurrence  of  the  alkaline  properties  at 
the  next  element,  potassium. 

Again,  although  the  groupings  shown  in  the  Table 
are  all  stable,  they  are  not  the  only  possible  arrange- 


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CHEMISTRY   OF  THE   MODEL .  ATOM    95 

ments  of  electrons.  Thus,  while  we  cannot  have  a 
ring  of  six  electrons  unless  there  is  at  least  one 
electron  inside  it,  we  may  conceivably  have  more 
than  this  without  disturbing  the  equilibrium.  Thus 
an  atom  with  ten  electrons  might  be  represented 
either  by  (8,  2)  as  in  the  Table,  or  by  the  grouping 
(7,  3).  The  latter  grouping  is  the  one  actually  seen 
in  the  photograph  (Fig.  20).  In  general,  one  of  these 
arrangements  would  be  more  stable  than  the  other, 
that  is  to  say,  its  energy  would  be  greater  and  it 
would  be  more  likely  to  survive.  At  certain  points, 
however,  the  different  configurations  might  be  so 
evenly  balanced  as  to  be  almost  equally  stable.  In 
this  case  we  should  have  a  series  of  elements  of 
almost  exactly  the  same  atomic  weight,  but  differing 
somewhat,  though  probably  not  markedly,  in 
properties  ;  a  case  corresponding  very  closely  to  the 
puzzling  series  of  rare  earths  which  occur  in  the 
middle  of  the  Periodic  Table. 

It  may  be  asked,  what  properties  can  be  asso- 
ciated with  a  grouping  of  electrons  in  a  sphere  of 
positive  electrification  ?  If  we  are  on  the  right 
track,  we  may  expect  sooner  or  later  to  be  able  to 
interpret  every  phenomenon  associated  with  the 
atom  in  terms  of  such  a  system.  But  this  is  a  far 
cry,  and  it  must  be  confessed  that  our  present  knowr- 
ledge  does  not  extend  very  far  in  this  direction. 
We  can,  however,  suggest  several  important  pro- 
perties which  may,  and  one  or  two  which  can  be 
proved  to  be  due  to  causes  of  this  kind. 

In  the  first  place,  we  may  almost  certainly 
include  all  those  forces  of  cohesion,  adhesion,  and 
the  like  which  go  by  the  name  of  molecular :  those 
attractions  which,  quite  insensible  at  any  appreci- 
able distance,  are  yet  at  distances  comparable  with 
the  diameter  of  a  molecule  strong  enough  to  rivet 
together  the  atoms  and  molecules  in  a  solid  so  firmly 
that  in  some  cases  it  requires  stresses  of  many  tons  to 


96  .MOLECULAR   PHYSICS 

the  square  inch  to  drag  them  asunder.  Since  these 
molecular  forces  determine  tenacity,  elasticity,  and 
melting  point  for  solids,  and  surface  tension  and 
vapour  pressure  for  liquids,  it  will  be  seen  that  a 
very  considerable  and  important  set  of  properties 
are  thus  brought  within  the  scope  of  our  hypothesis. 
The  most  probable  and,  indeed,  at  present,  the 
only  explanation  of  these  molecular  attractions,  is 
that  they  represent  the  resultant  force  between  the 
different  parts  of  the  two  electrical  systems  which 
make  up  the  atoms,  each  of  which  is  neutral  as  a 
whole.  Let  us  take  as  an  illustration  a  very  simple 
concrete  case.  Suppose  the  black  dots  in  Fig.  21 


o 

O       • 

•  o 
o     • 


FIG.  21.  —  DIAGRAM  TO  ILLUSTRATE  COHESION. 

represent  the  outer  rings  of  electrons  in  two  ad- 
jacent atoms,  and  that  the  effect  of  the  positive 
electricity  around  them  may,  for  the  sake  of  sim- 
plicity, be  regarded  as  .concentrated  in  the  white 
circles  between  them. 

Since  each  of  the  atoms,  as  a  whole,  is  electri- 
cally neutral,  the  attractions  and  repulsions  between 
the  different  parts  at  any  distance  which  at  all 
greatly  exceeds  the  diameter  of  the  atom  will  be 
vanishingly  small.  If,  however,  as  in  the  illustra- 
tion, the  two  atoms  are  brought  so  close  together 
that  their  distance  is  only  a  fraction  of  this  diameter, 
this  is  no  longer  the  case.  It  can  readily  be  shown 
that  the  atoms  will  turn  so  that  a  negative  electron 
in  the  one  is  faced  by  the  positive  portion  of  the 


CHEMISTRY   OF  THE  MODEL  ATOM    97 

other.  There  would  thus  be  an  attraction  between 
them  which  would  increase  with  great  rapidity  as 
the  distance  between  the  atoms  was  diminished. 
The  law  of  force  would  thus  be  similar  to  that 
actually  found  for  these  molecular  forces. 

The  magnitude  of  the  forces  obviously  depends 
on  the  number  and  arrangement  of  the  electrons  in 
the  atom.  A  complete  theory  of  cohesion  is  not 
possible  in  the  present  state  of  our  knowledge. 
There  is  little  doubt  that  it  will  be  found  to  proceed 
on  lines  not  very  different  from  the  explanation 
suggested  above. 

Although  our  methods  of  analysis  do  not  enable 
us  to  pursue  this  problem  further,  another  very 
important  characteristic  of  the  atom,  namely,  its 
emission  spectrum,  has  proved  more  amenable  to 
investigation.  The  evidence  obtainable  from  a 
study  of  spectral  lines  is  so  important  that  we  shall 
deal  with  it  more  fully  in  a  later  chapter.  For  the 
present  it  may  be  noted  that,  before  the  electron 
had  been  isolated  and  its  properties  determined  by 
direct  experiment,  it  had  been  shown  by  Lorentz 
that  the  systems  emitting  the  vibrations  which  con- 
stitute ordinary  light  were  negatively  charged 
particles,  and  further,  that  the  ratio  of  the  charge 
to  the  mass  was  of  the  order  of  1*7  X  io7.  It  was 
also  shown  that  these  same  electrons  were  the 
cause  of  the  absorption  of  light  and  its  dispersion  in 
transparent  media.  Thus,  practically  the  whole 
range  of  optical  phenomena  of  the  atoms  are  due 
to  the  electrons  which  they  contain. 

This  point  is  so  important  that  we  shall  return 
to  it  in  a  separate  chapter.  In  the  remainder  of 
the  present  chapter  we  will  confine  our  attention  to 
that  important,  fascinating  and  mysterious  quality 
of  the  atom  which  determines  its  chemical  pro- 
perties, namely,  valency. 

Ever  since  the  time  of  Berzelius,  the  view  has 
M.P.  7 


98  MOLECULAR   PHYSICS 

been  held  that  the  forces  binding  the  different  atoms 
together  within  the  molecule  were  electrical  in  their 
origin,  that,  for  example,  the  molecule  NaCl  was 
formed  by  the  mutual  attraction  of  a  positively 
charged  sodium  atom  for  a  negatively  charged  atom 
of  chlorine.  This  view  was,  of  course,  based  on  the 
phenomena  of  electrolysis.  When  an  electric  cur- 
rent is  passed  through  a  solution  of  sodium  chloride 
in  water,  it  is  found  that  the  sodium  makes  its  way 
to  the  negative  electrode,  the  chlorine  to  the  positive. 
Thus,  the  salt  behaves  as  if  the  sodium  atoms  bore  a 
positive  charge  and  the  chlorine  a  negative.  The 
conclusion  seems  irresistible,  that  the  force  binding 
together  these  opposites  in  the  same  molecule  is  the 
electrical  attraction  between  their  charges. 

It  was  found  necessary,  from  consideration  of 
the  electrolysis  of  such  compounds  as  CuCl2,  etc., 
to  assume  that  the  atoms  of  certain  elements  carried 
charges  amounting  to  twice,  three  times,  etc.,  the 
charge  carried  by  a  sodium  or  chlorine  atom,  and 
thus  the  notion  of  valency  arose,  the  valency  of  the 
element  being  the  number  of  times  its  charge  in  the 
ionic  state  exceeded  that  of  sodium  or  chlorine. 
For  elements  such  as  carbon  and  nitrogen,  which 
are  never  found  in  the  free  ionic  state,  the  valency 
was  deduced  from  their  chemical  analogy  to  ele- 
ments of  known  valency.  We  may  say,  then,  that 
positive  valency  represents  the  tendency  of  the 
neutral  atom  to  part  with  its  electrons,  while  nega- 
tive valency  is  the  tendency  of  the  neutral  atom  to 
absorb  electrons  into  itself  from  without.  If 
electro-positive  and  electro-negative  atoms  are  pre- 
sent together,  these  tendencies  can  both  be  satisfied 
by  the  mutual  interchange  of  one  or  more  electrons. 
The  passage  of  an  electron  from  one  atom  to  the 
other  will  make  the  former  positively  the  latter 
negatively  charged,  and  the  attraction  of  the  posi- 
tive atom  for  its  lost  electron  will  constitute  on  our 


CHEMISTRY   OF  THE   MODEL  ATOM    99 

hypothesis  the  force  of  chemical  combination 
between  the  two  atoms. 

Although  these  ideas  in  one  form  or  another  are 
as  old  as  Davy  and  Berzelius,  chemists  have  made, 
up  to  the  present,  little  direct  use  of  them,  finding 
the  notion  of  bonds  of  affinity  sufficient  for  all 
practical  purposes.  So  long  as  the  electric  charge 
was  regarded  as  something  apart  and  distinct  from 
the  atom  itself,  something  of  a  different  nature 
superadded  to  it  by  external  means,  the  electrical 
theory,  except  in  so  far  as  it  explained  the  phe- 
nomena of  electrolysis  in  which  it  had  its  rise,  was 
no  more  fundamental  than  the  theory  of  a  mys- 
terious chemical  bond. 

With  the  electron  theory  of  matter,  the  situation 
is  quite  changed.  It  is  evident  that  the  question 
whether  a  given  atom  will  tend  to  lose  or  gain 
electrons,  and  how  many  electrons  can  be  so  lost 
or  gained,  will  depend  upon  the  number  and  arrange- 
ment of  the  electrons  within  it,  and  the  forces  with 
which  they  are  retained  in  the  atom.  If  we  can 
determine  these,  and  if  we  can  show  that  they  lead 
to  a  similar  distribution  of  valency  with  atomic 
weight  to  that  actually  demanded  by  chemical 
considerations,  we  shall  feel  that  we  have  made  a 
very  hopeful  start  in  the  solution  of  this  funda- 
mentally important  question. 

In  the  first  place,  it  must  be  pointed  out  that  all 
the  electrons  in  the  atom  are  not  held  in  the  same 
way.  The  majority  of  the  electrons  are  too  firmly 
held  to  be  displaced  by  anything  short  of  a  dis- 
ruption of  the  whole  atom.  A  certain  number, 
however,  are  held  comparatively  loosely.  Optical 
experiments  have  shown  that  the  number  per  cubic 
centimetre  of  the  comparatively  mobile  eelctrons 
which  determine  the  dispersion  of  the  substance  is 
not  many  times  greater  than  the  number  of  atoms 
present.  Similar  results  are  obtained  from  a  con- 

7—2 


ioo  MOLECULAR   PHYSICS 

sideration  of  the  numbers  of  free  electrons  in  a 
metallic  conductor.  It  will  obviously  be  these 
free  electrons  that  determine  the  valency  of  the 
atom.  It  seems  very  probable  that  the  greatest 
number  of  these  that  any  atom  can  gain  or  lose  does 
not  exceed  eight,  and  it  may  be  noted  that  this  is  the 
greatest  charge  ever  found  to  be  carried  by  a  positive 
particle. 

Since  valency  is  a  property  of  the  simplest 
atoms,  it  seems  probable  that  the  valency  electrons 
form  the  innermost  ring  of  the  atomic  system.  Let 
us  suppose,  now,  that  the  maximum  number  of 
electrons  which  can  be  contained  in  this  inner  shell 
is  eight,  the  minimum,  of  course,  being  zero,  and 
let  us  suppose,  further,  that  there  is  a  tendency  in 
every  atom  to  give  this  inner  ring  either  its  maxi- 
mum or  minimum  value.  An  atom  with  an  inner 
ring  of  five  electrons  would  then  either  part  with  its 
five  valency  electrons,  in  which  case  it  would  have 
a  positive  charge  and,  consequently,  a  positive 
valency  of  five,  or  attract  three  more  electrons  from 
without,  making  up  its  complement  to  eight.  In 
this  case  it  would  be  electro-negative  in  character 
with  a  charge  and  a  valency  of  three.  It  will  be 
.noted  that  the  sum  of  the  two  valencies  is  equal  to 
the  maximum  number  of  particles  in  the  inner  ring, 
namely,  eight. 

Which  of  these  two  actions  would  take  place 
would  depend  on  the  nature  of  the  atoms  with  which 
it  was  placed  in  contact.  If  surrounded  by  atoms 
which  tended  to  part  with  electrons,  it  would  be 
electro-negative,  if  by  atoms  with  a  strong  attraction 
for  free  electrons,  it  would  eventually  give  up  some, 
or  all  of  its  five  to  the  stronger  atom  and  remain 
electro-positive  with  a  maximum  valency  of  five. 
The  atom  would  correspond  closely  to  such  a  sub- 
stance as  phosphorus,  which  forms  compounds 
such  as  PH3,  in  which  it  shows  a  negative  valency 


CHEMISTRY   OF  THE  , 

of  three,  while,  with  the  strongly  electro-negative 
element,  chlorine,  it  forms  compounds  such  as 
PCl3^and  PC15,  in  which  it  has  a  maximum  positive 
valency  of  five. 

To  compare  our  results  with  the  periodic  table, 
we  must  suppose  the  elements  of  Group  I.,  lithium, 
sodium,  etc.,  to  possess,  when  in  their  neutral  state, 
only  one  valency  or  free  .electron,  which  they  give 
up  with  the  greatest  readiness.  The  elements  of 
the  next  group  should  have  two  free  electrons  and  a 
positive  valency  of  two.  At  the  same  time,  there 
would  be  the  possibility  of  their  taking  in  sufficient 
electrons  to  bring  their  total  up  to  eight,  in  which 
case  they  would  possess  a  possible  maximum 
negative  valency  of  six.  I  am  not  aware  that  any 
compounds  have  been  prepared  in  which  this 
valency  is  exercised.  It  might,  in  any  case,  be 
expected  to  be  very  feeble. 

The  number  of  valency  electrons  in  the  atom, 
then,  increases  uniformly  as  we  pass  along  the  series, 
until  we  reach  the  halogens  with  a  total  number  of 
seven.  These  have  a  possible  positive  valency  of 
seven,  as  they  might  conceivably  lose  the  whole 
number  they  possessed.  This  valency  is  probably 
exercised  in  compounds,  such  as  I2O7.  As  they  con- 
tain very  nearly  the  maximum  number  possible, 
they  are,  however,  much  more  likely  to  acquire  the 
one  necessary  electron  to  make  their  total  up  to 
eight,  and  thus  act  as  strongly  electro-negative 
elements,  as  in  the  great  majority  of  their  stable 
compounds,  e.g.,  NaCl,  we  know  they  do.  From 
energy  considerations  we  should  expect  that 
the  number  of  electrons  in  the  inner  ring  would 
tend  to  that  stable  number  to  which  it  was  nearest 
to  begin  with.  Thus,  elements  possessing  fewer  free 
electrons  than  four  would  be  electro-positive,  those 
with  more  would  tend  to  make  their  complement  up 
to  eight,  and  be  electro-negative.  The  elements  of 


ica 


MOJlECULAR  PHYSICS 


the  carbon  group  (Group  IV.),  with  four  valency 
electrons  would  be  almost  indifferently  positive  or 
negative ;  as  we  find  them  to  be,  both  CO2  and  CH4, 
being  stable  compounds.  Our  complete  valency 
scheme  is  thus  represented  by  Table  VII.,  where 
the  Roman  numerals  indicate  the  group  in  the 
periodic  classification.  It  is  most  interesting  to  note 
that  Professor  Abegg,  in  a  very  illuminating  paper 
on  valency,  arrived  at  a  precisely  similar  scheme 
from  purely  chemical  considerations.  He  suggssted 
that  every  element  had  two  valencies,  a  normal  and 
a  contra  valency,  the  normal  being  supposed  to  be 
the  stronger.  The  positive  valencies  were  the  normal 

TABLE  VII. — TABLE  OF  VALENCIES  OF  THE  PERIODIC 
GROUPS. 


Group. 

i. 

ii. 

in. 

IV. 

V. 

VI. 

VII. 

Normal  valency    . 

+  i 

+  ? 

+  3 

_3 

—   2 

—  i 

±  4 

Additional    or 

contra-  valency  . 

-  7 

-  6 

-  5 

+  5 

+  6 

+  7 

for  elements  of  Groups  I.  to  III.,  the  negative  for 
Groups  V.  to  VII.,  Group  IV.  being  indifferently  plus 
or  minus.  The  sum  of  the  normal  and  contra 
valencies  for  any  element  was  eight.  It  will  be  seen 
that  this  suggestion  is  exactly  embodied  in  our 
theoretical  table. 

The  phenomena  of  variable  valency  and  valen- 
cies of  different  signs  have  no  difficulties  on  our 
hypothesis.  It  is,  in  fact,  exactly  what  we  should 
expect.  It  is  not  necessary  that  the  whole  of  the 
available  electrons  should  be  extracted  in  one  step. 
It  is  evident  that  the  work  done  in  extracting  an 
electron  from  the  atom  will  be  greater  for  the  second 
than  for  the  first,  and  it  is  quite  easy  to  imagine 


CHEMISTRY   OF  THE   MODEL  ATOM     103 


circumstances  under  which  the  ionising  force  was 
sufficient  to  produce  the  expulsion  of  one,  but  not 
of  two  electrons,  while  under  more  favourable 
conditions,  both  might  escape. 

The  inert  gases  of  the  helium  group  possess  no 
valency  and,  hence,  presumably,  no  free  electrons. 
We  have  already  remarked  that  the  phenomenon  of 
the  dispersion  of  light  is  due  to  these  free  electrons, 
which  are  thus  sometimes  spoken  of  as  dispersional 
electrons.  It  is  interesting  to  note,  in  support  of 
the  hypothesis  we  have  advanced,  that  the  dis- 

TABLE  VIII. — NUMBER  OF  FREE  ELECTRONS  IN  THE  ATOM 
DEDUCED  FROM  THE  DISPERSION  OF  LIGHT. 


Substance. 

Calculated 
Number  of 
Free  Electrons. 

Number 
Assumed 
(maximum 
positive  value). 

Hydrogen 

i'4 

I 

Calcium 

1*5 

2 

Carbon 

37 

4 

Siliccfe 

3*9 

4 

Oxygen 

.,. 

4*4 

6 

Chlorine 

• 

6'2 

7 

persion  of  light  in  helium  is  abnormally  small,  while 
that  of  the  halogen  gases,  which,  on  our  theory, 
possess  the  maximum  number  of  valency  electrons, 
is  very  large. 

Drude,  by  means  of  a  rather  abstruse  and  some- 
what approximate  calculation,  has  deduced  from 
these  considerations  the  number  of  free  electrons 
in  the  atoms  of  different  elements.  Some  of  the 
results  are  given  in  Table  VIII.  Remembering  that 
the  number  of  electrons  in  the  atom  must  be  an 
integer,  and  that  the  calculations  are  only  approxi- 
mate, his  calculated  values  seem  fully  to  bear  out 
the  assumption  we  have  made  above. 


104  MOLECULAR  PHYSICS 

Again,  our  hypothesis  explains  directly  the 
curious  connection  between  the  sign  of  the  valency 
and  electrical  conductivity.  With  the  exception  of 
hydrogen,  every  electro-positive  element  conducts 
electricity  when  in  the  solid  state.  This  fact  is  such 
a  commonplace,  that  an  explanation,  perhaps,  at 
first  sight,  hardly  seems  necessary.  On  any  other 
theory  of  valency,  however,  it  would  be  difficult  to 
account  for  this  invariable  co-existence.  On  the 
assumption,  however,  that  electro-positive  elements 
are  those  which  easily  give  up  electrons,  it  is  evident 
that  since  these  electrons  will  be  free  to  move  under 
the  electric  field,  these  elements  will  be  able  to  con- 
duct electricity,  while,  since  the  electro-negative 
elements  tend  to  absorb  electrons,  there  will  be  few 
electrons  present  in  them  in  a  free  state,  and  since 
the  atoms  themselves  are  not  able  to  move  through 
the  solid,  the  current  will  find  no  carriers,  and  so  will 
be  unable  to  pass. 

One  further  direct  deduction  from  our  hypo- 
thesis is  of  interest.  It  can  be  shown  that  when 
two  atoms  of  different  sizes  come  into  contact,  the 
attraction  of  the  smaller  atom  for  the  electrons  con- 
tained in  the  larger  exceeds  that  of  the  larger  atom 
for  the  electrons  in  the  smaller.  There  is  thus  a 
resultant  force  tending  to  drive  the  electrons  from 
the  larger  to  the  smaller  atom.  It  has  been  shown 
that  in  the  simplest  possible  case  an  electron  will 
actually  pass  between  two  similar  atoms  if  the 
radius  of  the  smaller  is  less  than  seven-tenths  that 
of  the  larger. 

Thus,  among  atoms  of  the  same  type,  those  with 
a  smaller  volume  will  tend  to  acquire,  those  with  a 
larger  volume  will  tend  to  lose,  electrons.  In  the 
same  group,  therefore,  the  elements  of  greater 
atomic  volume  will  be  more  electro-positive  (or  less 
electro-negative,  as  the  case  may  be)  than  the 
elements  with  the  smaller  atomic  volume.  In  any 


CHEMISTRY   OF  THE   MODEL  ATOM     105 

one  group  of  elements  the  atomic  volume  increases 
with  the  atomic  weight.  Hence,  we  arrive  at  the 
general  result,  that  the  electro-positiveness  of  the 
elements  in  any  group  increases  with  increasing 
atomic  weight.  This  relation  has  often  been  pointed 
out.  A  very  striking  example  of  it  is  seen  in 
Group  V.  of  the^  periodic  classification,  where  the 
lightest  element,  nitrogen,  is  usually  electro-nega- 
tive, while  the  heaviest,  bismuth,  is  generally 
electro-positive. 

We  have  now  traced  out  some  of  the  conse- 
quences of  the  hypothesis  that  valency  is  deter- 
mined by  the  number  of  loosely  bound  or  valency 
electrons  contained  in  the  atom,  these  electrons 
being  identical  with  those  which  determine  the 
dispersion  of  light.  We  have  also  made  the  addi- 
tional assumption  that  the  maximum  number  of 
such  electrons  which  can  be  contained  in  any  atom 
is  eight,  and  that  in  every  case  there  is  a  tendency 
to  make  this  number  either  eight  (negative  valency), 
or  zero  (positive  valency). 

This  latter  hypothesis  has,  it  must  be  confessed, 
somewhat  of  an  a  posteriori  air  about  it,  and  it  may 
be  interesting  to  investigate,  briefly,  whether  there 
is  any  property  of  electron  grouping  from  which 
this  apparently  arbitrary  assumption  can  be 
deduced. 

Qualitatively,  at  least,  we  can  show  that  some 
such  quality  is  a  direct  consequence  of  the  laws  of 
electron  groupings  which  we  have  formulated  above. 
It  was  shown  that  for  any  ring  or  shell  of  electrons 
to  persist,  there  must  be  contained  within  it  a  certain 
definite  number,  at  least,  of  other  electrons. 

Let  us  suppose  now,  that  for  an  outer  ring  of  A 
electrons  this  number  is  a,  while  for  a  ring  of  A  +  i 
electrons  it  is  b.  Consider  an  atom  with  a  ring 
of  A  electrons  having  n  other  electrons  within 
it  wThere  n  is  some  number  greater  than  a,  but  less 


io6  MOLECULAR  PHYSICS 

than  b.  By  suitable  means  we  may  extract  from 
this  atom  a  number  of  electrons  equal  to  n — a, 
without  destroying  the  equilibrium  of  the  outer 
ring  A.  If,  however,  we  succeeded  in  extracting 
one  further  electron,  the  system  would  become 
unstable  and  the  atom  would  collapse. 

Now  we  know  that  any  real  atom  is  a  very  stable 
structure  indeed.  Certain  atoms,  it  is  true,  owing 
to  circumstances  we  shall  have  to  consider  later, 
spontaneously  break  up  into  simpler  substances,  but 
there  is  no  known  agency  by  which  we  can  bring 
about  the  dissolution  of  an  atom  of  ordinary  matter. 
The  phenomena  of  radio-activity  have  furnished  us 
with  the  clue  to  our  failure  :  the  energy  required  is 
too  great.  On  the  other  hand,  the  energy  required 
to  extract  single  electrons  from  a  neutral  atom  has 
been  determined,  experimentally,  and  is  triflingly 
small.  A  single  a-particle,  for  example,  has  suffi- 
cient energy  to  produce  many  thousands  of  ions. 
Thus,  the  work  required  to  reduce  the  number  of 
electrons  in  the  atom  below  the  critical  value  a 
would  be  out  of  all  proportion  greater  than  that 
necessary  to  extract  the  electrons  above  this  number. 
In  effect,  the  value  a  would  be  a  barrier  which 
we  could  not  overstep. 

Similarly,  we  could  add  to  the  atom  sufficient 
electrons  to  make  its  number  up  to  b,  without 
bringing  about  any  change  in  atomic  structure. 
Beyond  that  point,  a  further  electron  would  neces- 
sitate an  outer  ring  of  A  +  z  electrons,  with  a  re- 
arrangement of  the  atomic  structure. 

Thus,  the  two  critical  values  a  and  b  constitute, 
as  it  were,  barriers  which  we  cannot  pass.  We  may 
extract  n  —  a  electrons,  at  most,  giving  the  element 
a  positive  valency  of  n  —  a,  or  we  may  add  b  —  n 
electrons,  giving  the  atom  a  negative  charge  and 
negative  valency  of  this  amount.  More  than  this 
we  cannot  achieve.  The  sum  of  these  two  valen- 


CHEMISTRY   OF  THE   MODEL  ATOM     107 

cies  is  obviously  b  —  a,  which  is  a  constant  for  all 
elements  with  a  ring  of  A  electrons. 

We  have  presented  the  argument  in  general 
terms,  rather  than  from  a  consideration  of  the  model 
scheme  in  Table  V.,  because  we  did  not  wish  to 
suggest  that  it  depended  in  any  way  upon  the 
numerous  simplifications  and  approximations  which 
were  necessary  in  calculating  that  table.  This 
granted,  however,  a  concrete  example  taken  from 
that  table  may  serve  to  make  the  argument  more 
clear. 

Consider  the  elements  with  an  outer  ring  of  seven- 
teen. We  have  lettered  them  from  /  to  s  in  Table  VI. 
The  number  of  electrons  within  the  ring  in  element  m 
is  twenty-six,  which  is  one  more  than  is  absolutely 
necessary  for  the  stability  of  the  ring.  Thus,  the 
element  m  might  lose  one,  and  only  one  electron 
without  any  violent  rearrangement  of  the  system 
taking  place.  Moreover,  as  the  system  is  not  much 
more  than  stable,  the  forces  retaining  the  electron 
within  the  atom  are  not  very  strong,  and  this 
electron  would  be  very  easily  displaced.  The 
element  m  would  thus  be  monovalent  and  strongly 
electro-positive.  The  next  element,  n,  could  lose  a 
total  of  two  electrons  without  derangement  of  the 
system.  It  would  thus  be  divalent  and  electro- 
positive, but  as  it  would  naturally  be  more  stable 
than  m,  its  activity  would  be  less  marked.  Thus, 
as  we  pass  along  the  series,  the  positive  valency 
increases  numerically  while,  at  the  same  time,  it 
decreases  in  intensity. 

At  the  other  end  of  the  series  the  element  r 
could  take  in  one  extra  electron  without  raising  its 
total  number  sufficiently  to  necessitate  an  outer  ring 
of  eighteen.  It  would  thus  be  monovalent  and 
electro-negative.  Theoretically,  it  might  also  lose 
six  electrons  and  be  hexavalent  and  electro-positive. 
From  energy  considerations,  however,  this  would 


io8 


MOLECULAR   PHYSICS 


only  occur  in  exceptional  circumstances.  Similarly, 
the  element  q  preceding  it  would  be  divalent  and 
electro-negative,  though  less  actively  so  than  r. 
Thus,  our  series  of  model  atoms  gives  us  a  valency 
system  very  similar  to  that  already  described. 

In  conclusion,  it  may  be  noted  that  the  electron 
theory  of  valency,  while  more  fundamental  and 
complete,  has  yet  a  very  close  resemblance  to  the 
"  bond  "  theory,  and  is  thus  capable  of  including  in 
itself  all  the  very  important  and  interesting  results 
which  have  been  achieved  on  that  hypothesis.  For 
consider  an  electro-positive  atom  which  has  lost  one 


FIG.  22. — STRUCTURE  OF  ETHANE. 

electron.  It  will  be  the  starting  point  of  a  Faraday 
tube  of  force,  which,  when  a  compound  is  finally 
formed,  will  end  up  upon  the  extra  electron  con- 
tained in  the  electro-negative  partner  of  the  com- 
bination. Similarly,  a  divalent  atom  would  be  the 
starting  point  of  two  such  tubes,  and  would  require 
two  monovalent  or  one  divalent  atom  for  its  satura- 
tion. Thus,  we  may  say  that  the  chemical  bonds 
represent  the  Faraday  tubes  linking  up  the  different 
atoms  in  the  molecule. 

There  is  this  difference,  however,  between  the 
two  theories,  that  while  a  bond  is  not  usually 
regarded  as  implying  direction,  a  Faraday  tube  is 
essentially  different  at  its  two  ends,  and  implies  a 


CHEMISTRY   OF  THE  MODEL  ATOM     109 

finite  difference  of  potential.  Take,  now,  the  case 
of  ethane,  C2H6.  Regarding  all  the  hydrogen  atoms 
as  positive,  three  Faraday  tubes  have  their  negative 
ends  upon  each  of  the  carbon  atoms  (Fig.  22). 
If  the  bond  between  the  carbon  atoms  is  a  Faraday 
tube  it  must  run  from  one  atom  to  the  other.  The 
atom  on  which  it  starts  will  then  have  a  total  nega- 
tive charge  of  2.e,  while  the  other  has  a  total  charge 
of  4.0.  The  two  carbon  atoms  are  thus  not  in 
precisely  the  same  electrical  state. 

No  change  in  properties  has  yet  been  observed, 
attributable    to    this    difference.      In  the  case    of 


FIG.  23. — STRUCTURE  OF  ETHYLENE. 

ethylene,  however  (Fig.  23),  where  the  difference 
between  the  atoms  is  more  marked,  one  carrying  a 
charge  of  4.0,  while  the  other  is  electrically  neutral, 
such  differences  have  been  noted.  Take,  for 
example,  the  property  of  the  refraction  of  light. 
It  has  been  found  that  the  refraction  produced  per 
molecule  by  many  organic  compounds  can  be 
calculated  by  assigning  certain  definite  values  to 
the  atoms  of  carbon,  hydrogen,  and  the  rest,  the 
molecular  refraction  of  any  compound  being  then 
equal  to  the  sum  of  the  values  for  all  the  separate 
atoms  which  go  to  make  up  its  molecule.  It  has 
been  found,  however,  that  if  the  carbon  atom  is 
present  in  the  ethylene  linking,  a  certain  additional 


no  MOLECULAR   PHYSICS 

amount  must  be  added  in  for  every  atom  so  linked 
up.  Thus,  the  atomic  refraction  of  the  carbon  atom 
is  apparently  not  the  same  in  its  neutral  as  in  its 
charged  state.  A  precisely  similar  result  is  obtained 
if  we  consider  other  additive  properties,  such  as 
molecular  volume.  Thus,  there  seems  to  be  a 
distinct  difference  in  the  properties  of  the  carbon 
atom  in  these  two  electrical  conditions. 

We  have  developed  this  subject  of  valency  at 
considerable  length,  because  it  is  one  of  the  most 
fundamental,  and,  at  the  same  time,  has  been  one 
of  the  most  mysterious  of  all  atomic  properties. 
While  it  would  be  idle  to  pretend  that  the  hypo- 
thesis which  we  have  advanced,  which  is  due,  in  the 
main,  to  Professor  Sir  J.  J.  Thomson,  is  at  present 
entirely  adequate  to  include  the  whole  of  these 
puzzling  phenomena,  it  does,  on  the  whole,  correlate 
so  successfully  the  more  fundamental  facts  of 
valency  that  we  cannot  but  feel  that,  at  any  rate, 
we  are  working  along  right  lines  and  may  look  with 
some  confidence  to  a  complete  solution  in  the 
perhaps  not  very  distant  future. 


CHAPTER  VII. 


THE  ATOM  IN  VIBRATION. 

IT  can  easily  be  shown  that  when  a  moving  electric 
charge  is  accelerated  or  retarded  in  any  way,  a  wave 
of  electro-magnetic  disturbance  radiates  out  through 
the  surrounding  space.  Consider  an  electron  with 
its  Faraday  tubes  moving  along  in  the  direction 
AB  (Fig.  24) .  If  the  electron  is  moving  with  uniform 


FIG.  24.- 


-PRODUCTION  OF  ELECTRO-MAGNETIC  DISTURBANCES 
BY  THE  STOPPAGE  OF  AN  ELECTRON. 


velocity  these  tubes  will  travel  along  with  the 
electron  as  if  they  were  rigidly  attached  to  it. 
Suppose,  however,  that  this  electron  on  reaching  a 
point  C  is  suddenly  stopped  in  its  career.  The  ends 
of  the  Faraday  tubes  attached  to  the  electron  are 
suddenly  brought  to  rest. 

Now  a    Faraday  tube  is  in  some  respects  very 
like  a  stretched  rope.     For  instance,  it  has  a  tension 


ii2  MOLECULAR   PHYSICS 

along  its  length,  and  possesses,  as  we  have  seen  in  a 
previous  chapter,  mass.  Thus,  just  as  when  one 
end  of  a  rope  is  jerked,  a  certain  definite  time 
elapses  before  the  displacement  reaches  the  other 
end,  so  a  displacement  in  a  Faraday  tube  does  not 
reach  all  points  of  it  simultaneously,  but  is  propagated 
along  it  with  a  definite  velocity.  In  the  case  of  the 

/T" 

stretched  rope  the  velocity  is  equal  to  /y  —  where 

T  is  the  tension  on  the  rope  and  m  its  mass  per  unit 
length.  On  similar  principles  it  can  be  shown  that 
the  velocity  of  a  disturbance  along  a  Faraday  tube 

is  equal  to      ,         where  ^  is    the    magnetic    per- 
V/^K 

meability  and  K  the  specific  inductive  capacity  of 
the  medium  through  which  the  disturbance  is 
travelling.  We  will  call  this  velocity  V. 

Now,  during  the  time  it  has  taken  for  the  jerk 
to  travel  from  the  electron  O  to  a  point  P,  the 
portion  of  the  tube  beyond  P,  not  having  received 
the  signal  that  the  electron  has  been  stopped,  has 
been  travelling  on  with  its  original  velocity  and  is 
now  in  the  position  P',  where  PP'  is  the  distance 
which  the  electron  would  have  gone  in  the  time 
taken  for  the  disturbance  to  travel  along  the  tube 
from  O  to  P.  Thus  a  kink  is  developed  in  the  tube 
which  travels  outward  along  it  with  the  velocity  V. 

The  bent  portion  of  the  tube  PP'  is  moving 
perpendicular  to  its  length  and  will  thus,  by  the 
principles  we  have  already  developed,  produce  a 
magnetic  field  in  the  medium  which  will  also  travel 
out  with  the  kink.  If  we  consider  all  the  tubes 
surrounding  the  particle,  it  will  be  seen  that  these 
bent  portions  will  form  a  kind  of  sheet  of  disturbance 
travelling  outwards  as  an  expanding  spherical  shell 
or  wave. 

If  we  can  determine  for  any  medium  the  values 
of  /x  and  K  in  the  same  system  of  units,  we  can 


THE  ATOM  IN  VIBRATION  113 

calculate  the  velocity  V  with  which  the  disturbance 
is  propagated  in  that  medium.  It  will  be  remem- 
bered that  the  electrostatic  system  of  units  was 
obtained  by  defining  K  the  specific  inductive 
capacity  of  air  as  unity.  The  electro-magnetic 
system  on  the  other  hand  assigns  this  value  to  ^  the 
magnetic  permeability  of  air.  The  comparison  of 
the  two  systems  can  best  be  performed  by  measuring 
the  capacity  of  the  same  condenser  according  to  both 
systems  of  units.  This  operation  is  described  in 
most  text-books  of  electricity,  and  its  details  are 
outside  the  scope  of  our  present  work.  The  results 
obtained  are,  however,  most  striking  and  important. 
The  result  of  a  long  series  of  experiments  at  the 
American  Bureau  of  Standards  extending  over 
several  years  has  given  a  value  for  V  of  2*997  X  io10 
cm.  per  second.  This  is,  within  the  limits  of 
experimental  error,  identical  with  the  best  deter- 
minations of  the  velocity  of  light,  which  have  given 
a  mean  value  of  2*998  xio10  cm.  per  second.  The 
agreement  between  the  values  obtained  for  the  two 
velocities  is  too  close  to  be  accidental.  It  affords 
a  convincing  proof  of  the  electro-magnetic  nature 
of  light. 

In  the  case  we  have  considered  where  the  particle 
is  suddenly  brought  to  rest  a  single  pulse  is  formed 
the  thickness  of  which  is  equal  to  the  distance 
through  which  the  disturbance  can  travel  in  the 
time  taken  to  stop  the  particle.  Such  pulses  are 
given  out  when  cathode  rays  in  a  discharge  tube 
impinge  on  a  solid  anticathode.  They  give  rise  to 
the  well-known  phenomena  of  Rontgen  or  X-rays. 

If  instead  of  stopping  the  particle  dead  we  cause 
it  to  oscillate  about  a  mean  position,  a  series  of  un- 
dulations will  be  set  up  in  the  Faraday  tubes  attached 
to  it,  such,  for  example,  as  are  seen  when  one  end 
of  a  long  rope  is  shaken  regularly  to  and  fro.  Thus 
a  series  of  electro-magnetic  waves  move  out  from  the 
M.P.  8 


H4  MOLECULAR  PHYSICS 

vibrating  electron,  their  frequency  being  equal  to 
the  number  of  vibrations  made  by  the  particle  per 
second.  Their  wave  length  is  equal  to  the  distance 
travelled  by  the  disturbance  during  the  time  of  one 
complete  vibration.  If  this  lies  between  -0004  and 
•0008  mm.  these  waves  will  produce  on  our  eyes  the 
impression  of  light.  This,  in  its  crudest  form,  is 
the  Faraday-Maxwell  electro-magnetic  theory  of 
light. 

Not  only  may  light  originate  in  the  vibration 
of  electrons;  all  our  experiments  drive  us  to  the 
conclusion  that  such  vibration  is  the  only  way  in 
which  light  can  be  produced.  Uncharged  matter 
is  apparently  quite  incapable  of  setting  up  any  kind 
of  disturbance  in  the  sether.  It  is  the  electric  charge 
which  serves  as  the  only  link  between  the  two. 

We  can,  however,  proceed  further  than  this. 
Modern  research  has  enabled  us  to  identify  with 
certainty  the  vibrating  systems  which  emit  the 
myriad  lines  in  the  spectra  of  the  elements  with  the 
electrons,  with  the  properties  of  which  we  are  now 
growing  familiar. 

Michael  Faraday,  with  almost  uncanny  prescience, 
seems  to  have  felt  that  the  relation  between  mag- 
netism and  light  must  be  of  the  closest,  and  sought 
for  it  with  unremitting  diligence.  It  is  one  of  the 
little  ironies  of  life  that  the  only  effect  which  he 
did  discover  (the  magnetic  rotation  of  the  plane  of 
polarisation)  was  one  of  the  very  few  phenomena 
which  the  theory  even  now  is  hardly  adequate  to 
explain.  The  effect  he  sought  for  was  not  discovered 
until,  more  than  thirty  years  later,  his  experiments 
were  repeated  with  stronger  magnetic  fields  and  far 
more  powerful  methods  of  spectrum  analysis  by 
Zeeman. 

He  found  that  if  a  source  of  light  was  placed 
between  the  poles  of  a  strong  electro-magnet  and  the 
light  emitted  was  examined  spec! rose opically,  a 


THE  ATOM   IN  VIBRATION 


curious  change  took  place  in  the  appearance  of  the 
different  lines  in  the  spectrum,  each  being  split  up  or 
decomposed  into  two  components  when  the  light 
was  viewed  along  the  lines  of  force  in  the  magnetic 
field,  or  three  when  viewed  at  right  angles  to  this 
direction. 

Let  us  consider  briefly  the  effect  of  applying  a 
magnetic  field  to  the  charged  particles  emitting  the 
vibrations  as  they  oscillate  about  their  mean 
positions.  In  general  the  path  described  by  the 
particle  will  be  somewhat  complicated.  We  can, 
however,  resolve  its  motion  in  the  usual  way  into 


Q 


FIG.  25.— ILLUSTRATING  THE  DECOMPOSITION  OF  A  HARMONIC 
MOTION  INTO  TWO  CIRCULAR  VIBRATIONS. 

vibrations  parallel  to  and  at  right  angles  to  the  lines 
of  force  in  the  magnetic  field.  The  vibrations 
performed  along  the  lines  of  the  field  will  be  unaltered 
by  the  application  of  the  field  since  the  latter  produces 
no  mechanical  effect  on  a  particle  moving  in  its 
own  direction. 

It  will  be  quite  different  with  those  vibrations 
which  are  executed  in  directions  at  right  angles  to 
this.  It  is  shown  in  works  on  mechanics  that  any 
harmonic  vibration  can  be  regarded  as  the  sum  of 
two  circular  motions  of  properly  chosen  amplitude 
and  phase.  For  example,  the  harmonic  motion  of  a 
particle  A  vibrating  along  the  straight  line  BC 

8—2 


n6  MOLECULAR   PHYSICS 

(Fig.  25)  is  exactly  equivalent  to  the  motions  of  two 
equal  particles  P  and  Q  describing  the  circles  shown 
in  the  diagram  with  equal  velocities  but  in  opposite 
directions. 

It  will  be  sufficient,  therefore,  and  will  lead  to 
no  loss  of  generality  if  we  consider  the  charged 
particles  as  describing  circles  at  right  angles  to  the 
magnetic  field,  under  the  action  of  forces  directed 
towards  the  centres  of  the  circles.  Since  the  motion 
of  the  charged  particles  is  now  everywhere  at  right 
angles  to  the  magnetic  field  there  will  be  a  mechanical 
force  acting  on  the  particles  which  will  be  everywhere 
at  right  angles  to  the  magnetic  field,  and  to  the 
direction  of  motion  of  the  particles.  A  little 
consideration  will  show  that  it  must  always  act  in 
the  line  joining  the  position  of  the  particle  at  any 
moment  to  the  centre  of  the  circle. 

Particles  such  as  P  and  Q  are,  however, 
describing  their  circles  in  opposite  directions.  Thus 
the  magnetic  force  will  be  in  one  case  directed 
towards,  in  the  other  away,  from  the  centre  of  the 
circle.  In  the  first  case  the  total  force  dragging  the 
particle  towards  the  centre  is  increased  ;  the  circle 
is  contracted  and  the  time  of  vibration  becomes 
more  rapid.  In  the  latter  the  effective  force  is 
diminished,  with  the  result  that  the  orbit  expands 
and  the  vibrations  become  slower. 

An  apple  whirling  round  at  the  end  of  a  string 
will  furnish  a  very  useful  analogy.  If  the  tension 
of  the  string  is  increased  the  apple  is  drawn  in  and 
its  revolutions  become  more  rapid.  If,  on  the  other 
hand,  the  tension  is  relaxed,  the  apple  takes  a 
wider  sweep,  while  the  time  it  takes  to  complete  a 
single  revolution  becomes  longer. 

Thus,  instead  of  all  the  particles  describing  their 
orbits  in  exactly  the  same  time  and  thus  producing 
light  of  one  frequency  only,  one  set  have  been 
accelerated,  the  other  retarded  by  the  magnetic 


THE  ATOM   IN   VIBRATION 


117 


field,  so  that  instead  of  a  single  line  the  spectroscope 
will  reveal  two,  one  on  each  side  of  the  original 
position  of  the  line.  By  optical  means  we  can 
distinguish  between  clockwise  and  counter  clockwise 
rotations,  and  can  thus  determine  which  of  the 
two  has  been  accelerated  and  which  retarded  by  the 
magnetic  field.  Since  the  effect  on  a  positive 
particle  would  be  exactly  the  reverse  of  that  on  a 
negative,  we  can  thus  determine  the  sign  of  the 


FIG.  26. — ILLUSTRATING  THE  ZEEMAN  EFFECT.  N,  S  ARE  POLES 
OF  ELECTRO-MAGNET.  A,  B  REPRESENT  THE  APPEARANCE 
OF  A  SINGLE  LINE  EMITTED  BY  THE  FLAME  AS  SEEN 
THROUGH  A  SPECTROSCOPE  PLACED  IN  THE  TWO  POSITIONS. 

charge  carried  by  the  vibrating  particle.  In  every 
case  so  far  examined  it  has  been  found  to  be 
negative. 

If  we  view  the  flame  along  the  lines  of  force, 
these  two  new  lines  are  the  only  ones  seen,  as  the 
vibrations  taking  place  in  the  line  of  sight  produce 
no  effect  on  the  eye.  If,  however,  we  look  across 
the  field,  the  vibrations  executed  along  the  lines  of 
the  field  will  also  produce  their  effect  in  the  spectro- 
scope, and  since  their  period  is  unaltered  by  the 
field  they  will  give  a  line  in  the  position  of  the  original 


n8  MOLECULAR   PHYSICS 

undecomposed  line.  Since  all  the  circular  paths 
are  being  now  viewed  end  on,  all  three  lines  will 
appear  to  be  plane  polarised.  These  results  are 
shown  diagrammatically  in  Fig.  26. 

This  in  its  simplest  form  is  exactly  the  effect 
discovered  by  Zeeman  in  1896.  He  found  that  if 
a  source  emitting  a  line  spectrum  were  placed  be- 
tween the  poles  of  a  very  powerful  electro-magnet 


FIG.  27. — THE  ZEEMAN  EFFECT.  (a)  UNDECOMPOSED  LINE. 
(6)  SAME  LINE  VIEWED  ALONG  THE  LINES  OF  FORCE  OF  A 
MAGNETIC  FIELD,  (c)  LINE  VIEWED  AT  RIGHT  ANGLES 
TO  LINES  OF  FORCE. 

and  viewed  with  an  interference  spectrometer  of 
high  resolving  power  the  line  was  split  up  into  three 
components  when  viewed  at  right  angles  to  the 
magnetic  field  and  into  two  when  seen  along  the 
lines  through  a  hole  in  the  pole  piece.  This  is  very 
well  shown  in  the  photograph  reproduced  in  Fig.  27. 
When,  at  the  suggestion  of  Lorentz,who  at  once  saw 
the  correct  explanation,  the  polarisation  of  the 


THE  ATOM   IN   VIBRATION  119 

different  components  was  examined,  it  was  found 
to  agree  exactly  with  that  described  above. 

-We  have  seen  that  these  observations  have  shown 
that  the  vibrating  system  is  negatively  charged. 
We  can,  however,  go  further  than  this.  Following 
up  the  argument  given  above  it  can  easily  be  shown* 
that  if  \a  and  Ac  are  the  wave  lengths  of  the  two 
outer  components  into  which  a  single  line  of  wave 
length  A0  is  split  up 


where  e/m  is  the  ratio  of  the  mass  to  the  charge  for 
the  particles  and  V  is  the  velocity  of  light.  Now 
Runge  and  Paschen  found  that  for  a  certain  series 

of  mercury  lines,  for  example,  the  value  of  -^—  -  —  - 

Ao 

was  2*14  for  a  magnetic  field  of  24,600  units,  while 
V  is  of  course  3  x  io10  cms.  per  second.  Substituting 
these  values  in  the  equation  we  have 

,          2-14  X  2  TT  X  3  X  io10 
e'm  ~-  24,600  -  or  r65  x  Io7" 

Considering  that  the  displacement  produced  by 
even  the  strongest  fields  amounts  generally  to  some- 
where about  one-fifth  of  the  distance  separating  the 
two  D  lines  of  sodium,  it  will  be  seen  that  this  result 
agrees  even  better  than  might  have  been  expected 
with  the  value  of  the  same  ratio  1-77  x  io7  deduced 
for  the  negative  electron  from  experiments  on 
cathode  rays.  The  identity  of  the  light-emitting 
systems  with  the  cathode  ray  particles  must  be 
regarded  as  established  beyond  all  challenge. 

Many  spectral  lines  show  the  Zeeman  effect  in 
this  simple  form.  Others,  however,  give  more  com- 
plicated effects,  some  of  the  lines  of  Molybdenum,  for 
example,  splitting  up  into  seventeen  and  even 
nineteen  components.  We  have,  in  assuming  that 

*  See  Appendix  C. 


120  MOLECULAR   PHYSICS 

the  vibrating  electron  executed  harmonic  vibrations, 
neglected  the  possibility  of  its  motion  being  disturbed 
by  the  forces  due  to  neighbouring  electrons  in  the 
same  atom.  If  these  are  not  negligible  complications 
ensue,  and  the  time  of  vibration  is  no  longer  indepen- 
dent of  the  direction  in  which  it  takes  place.  The 
matter  has  been  discussed  at  length  for  certain 
simple  systems  of  electrons  by  Professor  Sir  J.  J. 
Thomson,  and  his  paper  may  be  found  in  the 
Proceeding?  of  the  Cambridge  Philosophical  Society, 
Vol.  39,  by  any  who  are  interested  in  pursuing  the 
matter  more  deeply. 

The  lines  in  the  spectra  of  an  element  thus 
represent  the  different  modes  of  vibration  of  the 
electrons  connected  with  it.  It  might  seem  that 
with  a  complete  knowledge  of  these  periods  at  our 
disposal  it  should  be  possible  to  reconstruct  the  atom 
with  certainty.  Theoretically,  no  doubt,  this  should 
be  so.  The  mathematical  difficulties  are,  however, 
appalling,  and  only  in  the  case  of  a  few  very  simple 
systems  is  the  analysis  at  all  possible.  Thus  the 
results  to  be  looked  for  from  spectroscopy  are  at 
present  qualitative  rather  than  quantitative. 

Even  so,  however,  a  study  of  spectra  is  most 
luminously  suggestive.  A  careful  analysis  of  the 
innumerable  lines  which  are  dotted  apparently  at 
random  through  the  spectra  of  the  elements  has 
shown  that  they  are  by  no  means  the  confused 
jumble  of  periods  which  at  first  sight  they  appear  to 
be.  It  has  been  found  that  in  very  many  cases  they 
can  be  grouped  into  definite  series,  every  line  of 
which  can  be  obtained  by  substituting  particular 
whole  numbers  for  a  variable  quantity  "  m"  in  a 
general  equation  the  form  of  which  is  the  same  for 
all  elements. 

This  was  first  pointed  out  by  Balmer  for  the 
hydrogen  spectrum,  but  it  was  afterwards  shown  by 
Rydberg  that  Balmer's  equation  was  merely  a 


THE  ATOM   IN   VIBRATION  121 

particular  case  of  a  very  general  law  which  could  be 
stated  so  as  to  apply  to  all  the  elements  giving 
series  spectra.  He  showed  that  if  n  is  the  frequency 
of  the  vibrations  corresponding  to  a  given  line  (the 
frequency  is  the  number  of  vibrations  made  per 
second  by  the  particle  emitting  the  light)  then  the 
frequency  of  all  the  lines  in  a  given  series  can  be 
represented  by  the  equation— 

_N_ 
(m  +  /x)2 

the  different  lines  composing  the  series  being 
obtained  by  putting  m  equal  successively  to  the 
whole  numbers,  1,2,3,...  Nisa  constant  so 
universal  in  its  character  that  it  applies  not  merely 
for  all  the  series  of  a  given  element  but  for  all  the 
series  of  all  elements  giving  series  spectra  at  all. 
The  constants  n0  and  /x  differ  for  different  elements 
and  are  characteristic  of  the  particular  series. 

That  this  method  of  classifying  a  spectrum  is  no 
mere  mathematical  fiction  is  very  clearly  brought 
out  when  the  character  of  the  lines  making  up  a 
single  series  is  closely  observed.  It  is  found  that 
all  the  lines  of  a  single  series  are  exactly  similar  in 
appearance.  Thus  all  of  them  appear  sharp  and 
distinct  with  definite  clear-cut  boundaries,  or  else 
they  are  all  indistinct  and  diffuse.  The  two  types 
of  lines  are  never  associated  in  the  same  series. 
Again,  any  physical  change  which  we  bring  about  in 
one  of  the  lines  of  a  series  is  reproduced  simul- 
taneously in  all  the  others.  Thus,  all  the  lines 
split  up  in  the  same  way  under  the  action  of  a 
magnetic  field.  If  one  of  the  lines  is  broadened  by 
the  application  of  pressure  to  the  gas  emitting  the 
spectrum,  all  the  others  are  broadened  to  a  similar 
degree,  and  when  the  method  of  producing  the 
spectrum  is  altered,  all  the  lines  have  their  bright- 
ness either  enhanced  or  diminished  at  the  same 


122  MOLECULAR   PHYSICS 

time.  We  can  hardly  avoid  the  conclusion  that  they 
are  all  different  modes  of  vibration  of  the  same  system. 

An  analogy  may  make  this  clearer.  It  is  well 
known  that  when  an  organ  pipe  is  sounded  it  gives 
out  in  addition  to  its  fundamental  note  a  series  of 
overtones,  the  fullness  and  richness  of  the  organ 
notes  being  due  to  the  presence  of  these  extra  tones. 
In  such  a  simple  system  the  overtones  are  always 
harmonics,  that  is  to  say,  their  frequencies  are 
always  exact  multiples  of  the  lowest  mode  of 
vibration.  In  mathematical  language  we  can  say 
that  the  different  frequencies  are  obtainable  by 
substituting  various  whole  numbers  for  the  quantity 
m  in  the  equation,  n  =  m  .  n0. 

In  more  complicated  vibrators  the  relationship 
becomes  more  complicated  while  at  the  same  time 
the  importance  of  the  overtones  becomes  even  more 
pronounced.  In  the  case  of  a  sounding  bell  the 
relation  between  the  different  modes  of  vibration 
is  so  complicated  that  it  has  not  yet  been  completely 
worked  out. 

This  is  not  all,  however.  Not  only  do  the 
spectra  of  a  single  element  show  these  close  numerical 
relationships.  They  are  also  found  to  exist 
between  the  spectra  of  different  elements  belonging 
to  the  same  group  of  the  periodic  table.  The 
spectra  of  the  different  elements  of  the  alkali  metals, 
for  example,  are  so  closely  connected  that  it  is 
actually  possible  to  calculate  the  whole  spectrum 
of,  say,  rubidium  or  caesium,  from  that  of  potassium, 
and  a  knowledge  of  the  relative  atomic  weights  of 
the  three  elements.  The  spectrum  of  caesium  is 
practically  the  same  as  that  of  potassium  but  is 
shifted  bodily  towards  the  violet  end  of  the  spectrum. 
We  are  thus  driven  to  the  conclusion  that  the 
vibrating,  systems  in  the  two  cases  are  identical  in 
form,  and  differ  from  each  other  only  in  being  placed 
in  slightly  different  environments. 


THE  ATOM   IN   VIBRATION  123 

In  terms  of  our  model  atom,  if  we  regard  the 
series  spectra  as  being  given  out  by  the  inner  rings 
of  electrons,  these  rings  are  identical  for  the  three 
elements,  but  in  the  case  of  the  two  latter  the  extra 
outer  rings  added  on  to  increase  the  atomic  weight 
produce  some  alteration  in  the  external  forces  acting 
on  the  rings  and  so  cause  a  shift  in  the  absolute 
frequencies  of  the  vibrations  without  altering  the 
relation  between  them.  In  the  words  of  astro- 
nomical theory,  the  outer  electrons  perturb  the 
vibrations  of  the  inner  ring  without  destroying 
their  character.  Or,  returning  to  our  analogy  of 
the  bell,  it  is  the  same  bell  which  is  sounding  but  in 
a  somewhat  different  medium. 

One  difficulty,  a  very  formidable  one,  remains, 
and  may,  perhaps,  already  have  occurred  to  the 
reader.  The  spectra  of  many  of  the  elements  is 
exceedingly  complicated,  containing  in  some  cases 
many  hundreds  of  well-defined  lines.  A  contem- 
plation of  the  iron  spectrum  wrung  from  the  great 
American  spectroscopist  Rowland  the  exclamation 
that,  compared  with  an  atom  of  iron,  a  grand  piano 
must  be  a  very  simple  affair  indeed. 

We  have  seen,  however,  in  a  former  chapter  that1 
the  number  of  electrons  in  an  atom  is,  on  the  whole, 
not  very  large.  In  all  probability  the  hydrogen 
atom  contains  only  one  electron,  and  certainly  not 
more  than  three.  A  single  electron  has  only  three 
degrees  of  freedom  and  therefore  only  three  modes 
of  vibration,  and  in  the  simple  atom  these  three 
wrould  all  have  the  same  period  and  thus  coalesce 
into  a  single  line.  As  a  matter  of  fact,  the  ordinary 
spectrum  of  hydrogen  contains  a  fair  number  of 
lines  while  what  is  known  as  its  secondary  spectrum 
is  very  complicated.  The  difficulty  seems  at  first 
sight  almost  insuperable. 

To  solve  the  riddle,  Professor  Sir  J.  J.  Thomson 
has  hazarded  the  bold  but  almost  certainly  correct 


124  MOLECULAR   PHYSICS 

conjecture  that  the  lines  in  the  spectrum  of  hydrogen 
and,  indeed,  of  many  other  elements  are  not  emitted 
by  the  atoms  of  the  element  at  all  but  by  systems 
which  only  exist  when  the  gas  is  thrown  into  a 
luminous  condition.  When  we  consider  the  absolute 
identity  of  the  spectrum  of  an  element  whether 
situated  on  the  earth  or  away  on  the  furthest  star 
of  which  we  have  spectroscopic  data,  this  hypothesis 
may  seem  to  be  the  most  startling  we  have  yet 
advanced.,  It  is,  however,  not  without  a  very 
v  -considerable  experimental  basis. 

Consider  for  a  moment  the  phenomena  known  as 
selective  absorption  of  light,  of  which  the  well-known 
experiment  of  the  reversal  of  the  sodium  lines  is  a 
good  example.  If  white  light  is  passed  through 
sodium  vapour  enclosed  in  an  iron  tube  and  the 
transmitted  light  examined  with  a  spectroscope 
there  can  be  seen  across  the  ordinary  coloured 
spectrum  two  sharp,  dark  lines,  corresponding 
exactly  in  position  with  the  two  bright  lines,  which 
would  be  seen  if  the  sodium  were  raised  to  incan- 
descence. This  is  the  cause  of  the  dark  Fraunhofer 
lines  which  are  to  be  seen  crossing  the  spectrum  of 
the  light  from  the  sun. 

These  effects  are  due  to  a  form  of  resonance. 
The  sodium  atom  contains  systems  of  electrons 
which,  when  suitably  excited,  give  out  light  of  the 
frequency  corresponding  to  the  two  sodium  lines. 
To  use  an  analogy  from  sound  or  from  wireless 
telegraphy  the  sodium  atom  is  tuned  to  this 
frequency.  It  will  therefore  begin  to  vibrate 
violently  if  oscillations  of  this  period  fall  upon  it. 
In  doing  so  it  abstracts  the  energy  of  the  radiation 
in  tune  with  itself,  so  that  the  latter  is  very  rapidly 
absorbed,  while  light  of  frequency  remote  from  this 
passes  on  almost  unaffected.  Thus,  after  passing 
through  a  very  small  thickness  of  material  the  light 
is  robbed  of  all  the  constituents  which  have 


THE  ATOM   IN   VIBRATION 


125 


frequencies  corresponding  to  those  of  the  radiating 
systems  within  it.  Conversely  all  the  electronic 
systems  which  have  natural  periods  falling  within 
the  limits  of  the  visible  spectrum  must  produce  a 
dark  band  when  white  light  is  passed  through 
them. 

Now,  it  is  remarkable  that  such  absorption  lines 
are  not  seen  when  white  light  is  passed  through  a 


FIG.  28. — LADENBURG'S   EXPERIMENT. 

A,  discharge  tube  containing  hydrogen  at  high  pressure.  B,  dis- 
charge tube  containing  hydrogen  at  low  pressure.  C,  induc- 
tion coil  working  both  tubes.  Sp,  spectrometer  for  viewing 
the  light  transmitted.  The  inset  shows  the  appearance  seen 
in  spectrometer  when  the  tubes  are  working,  aa,  broadened 
band  due  to  hydrogen  in  A.  bb,  spectrum  due  to  the  tube 
B  alone.  The  dark  line  where  the-  two  bands  cross  shows 
the  reversal  of  the  line  by  the  systems  formed  in  B  by  the 
discharge. 


column  of  hydrogen,  or  indeed  of  most  other  simple 
gases.  There  are,  for  example,  no  dark  lines  to  be 
seen  in  the  spectrum  when  examined  after  passing 
through  a  long  tube  of  hydrogen  gas,  corresponding 
to,  say,  the  brilliant  lines  of  the  hydrogen  spectrum 
in  the  red  or  in  the  blue.  Indeed,  the  laws  of  the 
absorption  and  dispersion  of  light  in  hydrogen  are  so 
simple  that  they  can  be  explained  on  the  assumption 


126  MOLECULAR  PHYSICS 

of  a  single  absorption  band  far  away  beyond  the 

violet   end   of   the   spectrum.     This   is,    of   course, 

what  we  should  expect  from  the  simple  nature  of 

the  hydrogen  atom.     There  is  thus  no  escape  from 

I  the   conclusion  that  the  vibrating  systems  which 

;  emit  the  hydrogen  spectrum  are  not  present  in  the 

gas  in  its  normal  condition. 

A  very  interesting  experiment  made  not  long 
ago  by  Ladenburg  has  shown,  however,  that  they 
can  be  manufactured  in  the  gas  under  suitable 
conditions.  He  passed  the  light  from  a  very  bright 
discharge  in  hydrogen  at  fairly  high  pressure  through 
a  long  tube  of  hydrogen  at  much  lower  pressure, 
fitted  with  terminals  for  the  passage  of  a  discharge, 
and  examined  the  light  transmitted  with  a  spectro- 
scope. His  apparatus  is  indicated  very  di.agram- 
matically  in  Fig.  28.  The  effect  of  the  high  pressure 
on  the  discharge  is  to  widen  out  all  the  lines  in  the 
spectrum  so  that,  instead  of  a  narrow  line  a  broad 
band  of  light  is  seen  overlapping  the  original  line 
on  each  side.  When  there  was  no  discharge  passing 
through  the  long  tube  of  hydrogen  there  was  no  trace 
of  any  absorption  of  any  part  of  this  broadened  band. 
If,  however,  a  feeble  discharge  was  sent  through 
this  long  tube  of  gas  it  was  seen  that  the  centre  portion 
of  the  broad  line  corresponding  to  the  original  line 
and  hence  having  the  period  of  the  light  emitted  by 
the  tube  at  low  pressure  became  distinctly  less  bright 
than  the  outer  portions,  showing  that  the  long 
column  of  feebly  glowing  gas  was  now  absorbing 
from  the  light  emitted  by  the  brighter  hydrogen 
tube  those  wave  lengths  corresponding  in  period 
to  the  light  it  was  itself  giving  out.  There  are  some 
difficulties  in  the  experiment,  and  a  certain  syn- 
chronism of  the  two  discharges  seems  to  be  necessary 
for  its  success.  On  the  whole,  the  conclusion  seems 
irresistible.  The  hydrogen  line  spectrum  is  emitted 
by  systems  of  electrons  which  are  not  present  in  the 


THE  ATOM   IN   VIBRATION  127 

gas  in  its  normal  condition,  but  which  are  formed 
when  the  gas  is  thrown  into  a  luminous  state. 

Let  us  consider  for  a  moment  the  ways  in  which 
an  atom  can  be  made  to  emit  luminous  vibrations. 
Experiments  have  shown  that  for  an  atom  to  emit 
its  characteristic  spectrum  it  is  necessary  that  it 
should  be  in  a  region  of  intense  ionisation  or 
recombination.  It  seems  that  nothing  short  of 
driving  an  electron  into  or  out  of  the  atom  will 
suffice  to  set  in  vibration  the  light  emitting  systems 
of  electrons.  It  is  obvious  that  this  condition  is 
fulfilled  when  the  spectrum  is  excited  electrically, 
either  by  sparking  between  terminals  of  the 
substance  or  by  a  low  pressure  discharge  through  a 
gas.  It  is  interesting  in  this  connection  to  note  in 
the  latter  case  that  experiments  have  shown  that, 
in  the  dark  portions  of  the  discharge  the  ionisation 
is  very  feeble,  while  it  is  most  intense  in  the  brightest 
portions  of  the  positive  column.  The  ordinary 
method  of  producing  a  spectrum  by  placing  the 
substance  in  a  Bunsen  flame  is  also  merely  a  rough- 
and-ready  way  of  producing  ionisation  in  the 
substance,  Professor  H.  A.  Wilson  having  shown 
that  a  Bunsen  flame,  especially  if  it  contains  salt 
vapours,  is  the  seat  of  very  intense  ionisation. 

Consider  an  atom  placed  within  this  ionised 
space.  It  meets  the  ionising  agent  and  an  electron 
is  ejected,  leaving  the  atom  with  a  positive  charge. 
The  loss  of  this  electron  will  alter  the  forces  within 
the  atom  and  the  remaining  electrons  will  oscillate 
about  their  new  positions  of  equilibrium  before 
finally  settling  down.  These  vibrations,  if  of 
suitable  periods,  will  set  up  luminous  radiations 
and  give  rise  to  a  set  of  lines  in  the  spectrum.  The 
positively  charged  atom  is  now  surrounded  by  a 
cloud  of  negative  electrons  which  fill  the  surrounding 
space.  It  attracts  them  and,  normally,  one  would 
enter  to  take  the  place  of  the  lost  member.  If 


128  MOLECULAR   PHYSICS 

however,  the  mutual  kinetic  energy  of  the  two  is 
sufficient  the  electron  will  revolve  round  the  attracting 
atom  without  falling  into  it  in  exactly  the  same 
way  as  the  earth  revolves  around  the  sun.  The 
revolutions  of  this  electron,  being  isochronous,  will 
give  rise  to  a  single  line  in  the  spectrum  with  a 
period  corresponding  to  the  time  taken  by  the 
electron  to  describe  the  circle. 

If  the  law  of  force  between  the  atom  and  the 
electron  were  the  simple  one  of  the  inverse  squares, 
an  orbit  of  any  size  would  be  possible  under  suitable 
conditions.  Taking  into  account  the  fact  that  the 
electron  is  losing  speed  owing  to  the  fact  that  it  is 
all  the  time  radiating  away  its  energy  in  the  form 
of  light  waves,  it  will  be  gradually  drawn  nearer  and 
nearer  the  atom  so  that  its  path  would  be  a  sort  of 
spiral  ending  up  in  collapse  into  the  atom.  Since 
slightly  different  times  would  be  occupied  in 
describing  each  part  of  the  curve  the  spectrum  thus 
produced  would  be  continuous. 

The  neighbourhood  of  the  electrons  within  the 
atom  and  their  repulsion  of  the  external  one  would 
complicate  the  simple  law  of  force,  and  in  general 
the  attraction  of  the  atom  for  its  satellite  would 
depend  not  only  on  the  distance  but  also  on  the 
direction  of  the  line  joining  the  satellite  to  the  atom. 
The  actual  law  of  force  would  thus  depend  upon  the 
number  and  arrangement  of  the  electrons  within  the 
atom,  just  as  much  as  if  the  electron  were  revolving 
inside  it. 

Sir  George  Darwin,  in  his  monumental  work  on 
Periodic  Orbits  has  shown  that,  if  the  single 
system  of  a  satellite  revolving  round  its  planet  is 
disturbed  by  the  presence  of  a  third  body,  the  number 
of  orbits  which  the  satellite  may  describe  is  no 
longer  infinite,  but  that  there  are  certain  regions 
through  which  the  particle  must  not  pass  if  it  is  to 
continue  to  revolve  as  a  satellite  around  the  planet. 


THE  ATOM   IN   VIBRATION  129 

In  the  simple  case  considered  by  Darwin  this  space 
did  not  quite  enclose  the  planet,  but  in  more  compli- 
cated cases  such  as  we  have  to  deal  with  when  we 
come  to  a  consideration  of  the  atom,  hg  was  of  the  ^ 
opinion  that  it  might  very  well  take  the  form  of 
a  series  of  closed  rings  surrounding  the  atom. 
In  this  case  there  would  be  a  series  of  separate  rings 
in  which  alone  the  electron  could  revolve,  and 
each  of  which  it  would  describe  in  a  definite  time 
peculiar  to  that  ring.  Each  of  these  rings  would 
thus  give  rise  to  a  separate  line  in  the  spectrum. 
Since  the  atom  would  only  attract  one  electron  at 
a  time  each  atom  would  at  one  time  be  only 
emitting  one  of  these  extra  lines. 

These  systems  would,  of  course,  not  be  permanent, 
as  the  electron  would  constantly  be  losing  energy 
by  radiation.  After  a  time  its  energy  would  fall 
below  that  necessary  to  keep  it  in  rotation  in  the 
ring  it  was  describing,  and  it  would  collapse  through 
ring  after  ring,  until  finally  it  was  reabsorbed  into 
the  atom.  Fresh  systems  would,  however,  be 
constantly  being  formed  in  the  ionised  gas,  and  the 
supply  would  be  kept  up  as  long  as  the  exciting 
conditions  were  maintained. 

The  return  of  the  lost  electron  into  the  atomic 
fold  would  obviously  stir  up  fresh  vibrations  among 
the  electrons  already  present.  Since  the  atom  is 
now  neutral  and  not  positively  charged  as  it  was 
when  the  electron  left  it  these  vibrations  would  not 
have  the  same  periods  as  those  set  up  when  the 
electron  was  expelled.  There  is  some  evidence  for 
the  suggestion  that  the  vibrations  corresponding  to 
the  return  of  the  electron  form  the  band  spectrum  of 
the  element,  while  those  set  up  on  its  expulsion, 
together  with  those  due  to  the  special  systems,  make 
up  the  different  series  of  line  spectra. 

Very    recently    an    ingenious     Danish     mathe- 
matician, Dr.  Bohr,  has  worked  out  mathematically 
M.P.  o 


130  MOLECULAR  PHYSICS 

a  theory  of  spectra  very  much  on  the  lines  described 
above,  and  has  in  this  way  obtained  a  formula  for 
the  spectral  series  identical  in  form  with  the 
empirical  formula  of  Rydberg  which  we  have  already 
discussed.  He  has  from  his  theory  deduced  an 
expression  for  the  universal  constant  N  of  Rydberg's 
equation  in  terms  of  the  mass  and  charge  on  an 
electron  and  other  known  physical  quantities,  which 
gives  a  numerical  value  for  that  quantity  within 
about  5  %,  of  the  value  obtained  from  direct  spectro- 
scopic  observations.  His  assumptions  will  require 
further  consideration  before  they  can  be  unreservedly 
adopted.  They  appear  to  involve  the  abandonment 
not  merely  of  Newtonian  mechanics,  but  also  of  the 
ordinary  Faraday-Maxwell  electro-magnetic  theory. 
The  closeness  of  the  agreement  between  the  results 
of  'the  theory  and  of  experiment  is,  however,  at 
least  remarkable,  and  seems  to  show  that,  at  any 
-rate  in  its  general  outlines,  the  theory  of  the  origin 
of  spectra  which  we  have  propounded  above  is  a 
step  in  the  right  direction. 

We  have,  however,  wandered  far  from  the  solid 
certainties  of  the  Zeeman  effect  and  its  consequences, 
with  which  we  commenced  this  chapter,  into  the 
dark  and  mysterious  hinterland  where  science  is  in 
the  making.  In  a  few  more  years  we  may  hope  that 
this  will  be  transformed  into  plain  and  open  ground. 
At  present  we  must  pause  here,  lest  we  lose  ourselves 
altogether  in  a  quagmire  of  fascinating  but  ground- 
less speculations. 


CHAPTER   VIII. 
THE  MOLECULAR  THEORY  OF  MATTER. 

WE  have  now  surveyed  very  briefly  what  is 
known  and  surmised  of  the  nature  and  properties  of 
the  atom  and  molecule.  In  the  brief  space  of  the 
present  chapter  let  us  indicate  one  or  two  of  the  many 
points  of  interest  which  arise  when  we  come  to  con- 
sider the  molecule,  not  as  standing  by  itself,  but  as 
massed  together  in  myriads  to  form  a  fragment  of 
what  we  know  as  matter. 

In  solids,  we  must  regard  the  molecules  as 
fixed  relatively  to  each  other,  and  we  have  in  an 
earlier  chapter  considered  briefly  the  nature  of  the 
molecular  forces,  cohesion,  adhesion,  and  the  like, 
which  bring  about  this  result.  But  though  the 
molecules  are  fixed,  in  the  sense  that  they  are  not 
free  to  move  about  in  the  solid,  we  cannot  consider 
them  as  being  altogether  motionless.  Every  body, 
unless  it  is  at  the  absolute  zero  of  temperature  (a 
temperature  which  has  not  yet  been  reached  in 
any  experiment,  although  the  brilliant  researches 
of  Kamerlingh  Onnes  have  brought  us  within  4° 
of  it),  contains  a  certain  definite  amount  of  heat. 
Now  heat  is  merely  energy  in  a  molecular  form. 
The  work  which  we  do  in  raising  the  temperature 
of  a  substance  is  in  reality  spent  in  increasing  the 
energy  of  the  individual  molecules  of  the  substance, 
and  thus  in  every  body  which  is  not  at  the  absolute 
zero,  the  molecules  must  be  in  some  sort  of  motion, 
the  rapidity  of  which  increases  as  the  temperature 
is  raised. 

9—2 


132  MOLECULAR  PHYSICS 

The  molecules  of  the  solid  are  not  free  to  move 
from  their  positions,  but  two  forms  of  motion  are 
possible  to  them.  They  may  either  spin  round 
like  a  top,  or  oscillate  backwards  and  forwards 
about  their  mean  position,  like  the  bob  of  a  pen- 
dulum, or  like  a  heavy  weight  suspended  by  an 
elastic  cord. 

In  the  case  where  the  molecule  is  a  system  made 
up  of  two  or  more  atoms,  both  these  kinds  of  motion 
take  place.,  The  atoms  spin  round  their  common 
centre  at  a  rate  which  increases  as  the  body  gets 
hotter,  while  at  the  same  time  the  molecule  as  a 
whole,  oscillates  backwards  and  forwards  about  its 
mean  position  with  ever-increasing  amplitude.  If, 
however,  the  molecule  consists  of  a  single  atom, 
only  the  latter  form  of  motion  seems  to  be  possible, 
all  the  evidence  going  to  show  that  thermal  energy 
is  unable  to  set  a  single  atom  spinning  about  its 
own  centre. 

For  the  sake  of  simplicity  we  will  consider  the 
case  of  the  non-atomic  molecule,  where  the  thermal 
energy  is  all  used  in  the  second  kind  of  motion. 
As  the  body  gets  hotter  and  hotter,  the  molecule 
moves  faster  and  faster,  and  the  swings  which  it  takes 
on  each  side  of  its  normal  position  get  larger  and 
larger.  The  molecular  forces  which  keep  it  in 
position,  however,  fall  off  very  rapidly  as  the  dis- 
tance between  the  neighbouring  molecules  is 
increased,  while  at  the  same  time  the  force  required 
to  retain  the  molecule  in  position  increases  with 
every  increase  in  velocity.  Hence,  sooner  or  later, 
a  point  is  reached  when  the  molecular  forces  are 
no  longer  able  to  retain  the  atoms  in  position.  The 
solid  loses  its  cohesion  and  its  rigidity.  In  other 
words  it  melts. 

It  is  obvious  that  melting  sets  in  when  the  tem- 
perature is  just  sufficient  to  give  the  molecules  the 
necessary  minimum  of  velocity  to  overcome  the 


MOLECULAR  THEORY   OF  MATTER     133 

molecular  forces  retaining  them  in  position,  that  is 
to  say,  it  will  be  a  constant  for  any  definite  substance. 
Also  as  work  must  be  done  to  break  down  these 
inter-molecular  bonds  it  is  evident  that  energy 
must  be  supplied  to  the  body  in  the  form  of  heat 
to  enable  it  to  melt.  This  is  the  latent  heat  of 
liquefaction. 

Though  the  molecule  has  broken  its  old  bonds, 
it  is  still  within  the  range  of  molecular  attraction 
of  many  of  its  neighbours,  and  has  hardly  escaped 
from  one  cluster  before  it  is  attracted  into  another. 
Its  rate  of  progress  is  thus  comparatively  slow. 
In  time,  however,  any  given  group  of  molecules 
will  be  found  dispersed  throughout  the  whole  of 
the  liquid  and  thus  diffusion  is  brought  about. 

Consider  now  the  state  of  affairs  at  the  surface 
of  the  liquid.  Every  molecule  as  we  know  attracts 
every  other  molecule  which  may  happen  to  be 
within  a  certain  distance  from  it  which  we  denote 
as  the  sphere  of  molecular  attraction.  In  the 
body  of  the  liquid,  this  attractive  force  is  more  or 
less  neutralised  by  the  fact  that  the  molecule  we 
are  considering  is  surrounded  on  all  sides  by  others, 
all  pulling  in  different  directions.  Hence  the  com- 
bined effect  is  practically  zero.  At  the  surface, 
however,  all  the  molecules  are  below  it,  and  there 
are  none  above  to  neutralise  the  force  which  they 
exert.  There  is  thus  a  strong  downward  force 
tending  to  drag  the  molecule  into  the  surface. 
This  force  makes  itself  manifest  in  the  phenomenon 
known  as  surface  tension  or  capillarity. 

A  molecule  will  thus  require  a  definite  and  in 
most  cases,  a  considerable  velocity  to  succeed  in 
escaping  from  the  surface  of  the  liquid.  Now  the 
mean  velocity  of  the  molecules  depends  only  on 
the  temperature,  and  is  fixed  for  any  given  sub- 
stance when  the  temperature  is  known.  The  actual 
velocity  of  any  given  molecule  at  a  given  instant 


134  MOLECULAR   PHYSICS 

may,  however,  differ  very  considerably  from  this 
average  speed.  The  molecules  in  the  liquid  are 
constantly  bumping  against  each  other,  and  at 
every  collision  one  of  the  molecules  will  probably 
gain  speed,  and  the  other  lose  it,  and  a  difference 
in  velocity  is  thus  set  up.  The  law  of  the  distribu- 
tion of  speeds  among  an  infinite  number  of  colliding 
molecules  has  been  worked  out  by  Maxwell,  for  the 
simpler  case  of  a  gas,  and  is  known  as  Maxwell's 
law.  He  showed  that  at  any  given  instant  the 
great  majority  of  the  molecules  would  have  velo- 
cities not  widely  removed  from  the  average,  but 
that  there  would  always  be  a  few  which,  owing  to 
special  circumstances,  would  have  velocities  very 
much  greater,  and  others  with  velocities  very  much 
less,  than  the  normal  value. 

Thus  for  oxygen  at  0°  C.,  in  which  the  mean 
velocity  of  the  molecules  is  425  metres  per  second, 
out  of  every  1,000  molecules  of  the  gas,  about  half 
have  velocities  between  300  and  500  metres  per 
second,  but  there  are  77  with  a  velocity  greater 
than  700  metres  per  second,  and  30  with  a  velocity 
greater  than  900  metres  per  second. 

The  case  of  a  liquid  is  much  more  complicated 
than  that  of  a  gas,  but  there  is  no  doubt  that  a 
similar  state  of  affairs  prevails  in  the  liquid  state 
also.  Hence,  even  at  temperatures  far  below  the 
boiling  point  of  the  liquid,  there  will  be  a  few 
molecules  which  have  temporarily  sufficient  speed 
to  escape  from  the  attraction  of  the  mass  of  liquid 
below  them. 

Thus  even  at  low  temperatures,  a  certain  number 
of  molecules  escape  every  second  from  the  free 
surface  of  the  liquid.  If  the  space  above  the 
liquid  is  free  there  will  thus  be  a  constant  evapora- 
tion going  on  until  all  the  liquid  disappears  into 
vapour. 

If,  however,  the  liquid  is  contained  in  a  closed 


MOLECULAR  THEORY   OF   MATTER     135 

vessel,  the  escaping  molecules  are  unable  to  get 
away  altogether  and  after  perhaps  many  reflections 
at  ^the  enclosing  walls  will  sooner  or  later  strike 
the  surface  of  the  liquid  and  be  reabsorbed.  The 
number  so  returned  to  the  liquid  will  depend  on 
the  number  of  molecules  present  in  the  vapourous 
state  above  the  liquid.  Evaporation  will  go  on 
until  the  number  of  molecules  in  unit  volume  of  the 
vapour  is  so  great  that  the  number  returned  per 
second  is  exactly  equal  to  the  number  which  escape 
per  second  owing  to  their  high  velocity.  Thus  for 
every  temperature  there  will  be  a  corresponding 
vapour  pressure  which  will  be  constant  for  that 
temperature  and  that  pressure.  If  the  temperature 
is  raised,  the  average  speed  of  the  molecules  is 
increased,  and  more  of  them  will  attain  a  velocity 
sufficient  to  enable  them  to  escape  from  the  surface. 
The  vapour  pressure  thus  rises.  When  the  vapour 
pressure  reaches  that  of  the  atmosphere  the  liquid 
will  begin  to  boil,  and  if  the  supply  of  heat  is  main- 
tained, will  all  pass  into  the  state  of  a  gas. 

The  difference  between  a  liquid  and  a  gas  is 
that  in  the  latter  all  the  molecules  are  moving 
with  sufficient  speed  to  escape  completely  from  the 
attraction  of  their  neighbours,  and  are  thus  able 
to  avoid  those  molecular  aggregations  which  take 
place  in  the  liquid  state.  On  this  account  the 
behaviour  of  a  molecule  in  a  gas  lends  itself  much 
more  readily  to  mathematical  analysis  than  the 
more  complicated  phenomena  of  the  liquid  and 
solid  states.  The  kinetic  theory  of  gases  has  been 
very  completely  worked  out  by  Maxwell,  Clausius, 
and  their  successors.  Unfortunately,  even  with  the 
simplifications  thus  introduced,  the  theory  needs 
considerable  mathematical  ability  for  its  elucida- 
tion, and  does  not  lend  itself  at  all  readily  to  non- 
mathematical  treatment. 

The  pressure  which  a  gas  exerts  on  its  boundaries 


136  MOLECULAR  PHYSICS 

is  made  up  of  the  innumerable  shocks  given 
to  the  bounding  walls  by  the  many  impacts  upon 
them  of  the  molecules  of  the  gas,  which  are  moving 
as  we  have  seen  with  considerable  speeds.  It  will 
obviously  depend  on  the  number  of  molecules 
present  per  unit  volume,  and  the  speed  with  which 
they  are  moving.  The  higher  the  temperature,  the 
faster  the  molecules  move,  and  the  greater,  there- 
fore, will  be  the  pressure  they  exert.  It  can  be 
shown  that  this  pressure  is  simply  proportional  to 
the  temperature,  if  we  begin  to  measure  the  latter 
not  from  the  freezing  point  of  water,  but  from  the 
absolute  zero  of  temperature,  that  is,  the  tempera- 
ture at  which  the  molecules  would  all  be  reduced  to 
rest.  This  temperature  is  about  273°  below  the  zero 
on  the  Centigrade  scale. 

Again,  if  we  halve  the  volume  occupied  by  the 
gas,  we  double  the  number  of  molecules  present  in 
every  cubic  centimetre,  and  hence  double  the 
pressure  which  they  exert  on  the  enclosing  walls. 
The  pressure  is  thus  inversely  proportional  to  the 
volume  occupied  by  the  gas  and  directly  propor- 
tional to  its  absolute  temperature  ;  thus,  if  P  is 
the  pressure,  V  the  volume  and  T  the  temperature, 
of  a  given  mass  of  substance  in  the  gaseous  form, 
P  .V/T  is  a  constant.  This  is  the  well-known  gas 
equation  embodying  the  laws  of  Boyle  and  Charles. 

These  laws  are  obeyed  approximately  by  all 
gases,  but  perfectly  by  none.  We  have  assumed 
in  calculating  the  formula  that  the  molecules  exert 
no  attraction  upon  each  other  in  the  gaseous  state. 
This  is  of  course  only  approximately  true.  Hence 
the  velocity  with  which  the  molecules  strike  the 
boundary  is  always  a  little  smaller  than  the  normal 
velocity  at  that  temperature,  owing  to  the  attraction 
of  the  molecules  behind  it.  This  effect  will  obviously 
be  greater  if  the  molecules  are  closely  packed  together 
than  if  they  occupy  a  large  volume.  It  has  been 


MOLECULAR  THEORY   OF   MATTER     137 

shown  that  to  get  the  true  pressure  we  must  add 
to  the  observed  pressure  an  amount  equal  to  #/V2, 
where  a  is  constant  for  a  given  gas. 

Again  the  actual  space  in  which  the  molecules 
are  free  to  move  is  less  than  the  whole  space  of 
the  vessel,  owing  to  the  fact  that  the  molecules 
are  not  mere  mathematical  points,  but  have  a 
definite  volume  of  their  own.  Thus  if  b  is  the 
whole  volume  occupied  by  all  the  molecules  in  a  gas, 
the  actual  free  space  in  which  they  are  free  to  move 
is  not  V  the  volume  of  the  vessel,  but  V  —  b. 

To  be  accurate,  therefore,  we  should  write  our 
gas  equation  in  the  form 


where  R  is  a  constant  for  the  gas. 

This  equation  was  first  given  by  Van  der  Waals, 
and  is  found  to  represent  the  behaviour  of  real 
gases  with  a  considerable  degree  of  accuracy.  In 
fact  it  is  even  capable  of  representing  with  some 
degree  of  success  the  transition  state  from  liquid  to 
gas.  It  has  the  further  advantage  that  it  offers 
us  a  simple  method  for  determining  the  one  mole- 
cular dimension  with  which  we  are  still  unacquainted, 
namely,  the  radius  of  the  molecule. 

By  accurate  experiments  on  the  behaviour  of  the 
gas  under  varying  conditions,  we  can  determine  the 
value  of  the  constant  b  in  any  given  case.  Since 
one  molecule  cannot  pass  between  two  others  if  the 
space  between  them  is  less  than  the  diameter  of  a 
molecule,  the  volume  b  occupied  by  the  molecules 
in  the  gas  will  be  somewhat  greater  than  the  sum  of 
their  individual  volumes.  If  r  is  the  radius  of  each 
molecule,  and  N  the  total  number  of  molecules 
present  in  the  gas,  a  number  which  we  have  already 
determined  it  can  be  shown  that 


138 


MOLECULAR   PHYSICS 


assuming  that  the  molecules  are  spheres.  In  com- 
pound gases  where  there  are  several  atoms  in  the 
molecule  this  can  hardly  be  the  case,  but  in  the  case 
of  monatomic  gases  where  the  atom  is  also  the 
molecule,  it  seems  a  probable  assumption.  Hence 
knowing  N,  we  can  calculate  the  value  of  r  the  radius 
of  the  molecule  of  the  gas  we  are  considering.  A 
few  of  the  values  so  obtained  are  given  in  Table  IX. 
It  will  be  seen  that  they  are  of  the  order  of  io~8  or 
one  hundred  millionth  of  a  centimetre.  The  radius 
of  an  electron  is  io~13  cms.,  or  about  one  ten  thou- 
sandth part  of  this.  The  size  of  an  electron  thus 

TABLE  IX. 

The  Radius  of  the  Molecule. 


Substance. 

From  Van  der  Waals' 
Equation. 

From  the  Viscosity. 

From  the  Thermal 
Conductivity. 

Hydrogen 

i-i6x  io—  *cm. 

1*23  x  io—  8cm. 

i*2o^<  io—  8cm. 

Helium    . 

i'i5 

1-09 

— 

Nitrogen  . 

1*76 

J'75 

1-66 

Oxygen   . 

— 

1*70 

I*55 

Argon 

i'43 

1-68 

Carbon 

dioxide  . 

1-70 

2-09      ,;•„  •-- 

2-16 

bears  to  the  size  of  the  molecule  in  which  it  moves 
very  much  the  same  relationship  that  the  diameter 
of  our  earth  bears  to  the  diameter  of  its  orbit  round 
the  sun.  A  molecule  is  therefore  a  system  very 
similar  in  its  relative  dimensions  to  the  solar  system 
but  on  an  infinitesimal  scale. 

The  kinetic  theory  affords  other  methods  of 
estimating  the  dimensions  of  a  molecule,  but  their 
theory  is  too  complicated  to  be  attempted  in  the 
space  that  remains.  The  results  obtained  are  in- 
cluded for  the  sake  of  comparison  in  Table  IX. 
The  second  column  of  figures  gives  the  value  of  the 


MOLECULAR  THEORY   OF  MATTER     139 

radius  deduced  from  considerations  of  the  viscosity 
of  the  gas  ;  the  last  column  the  value  deduced 
from  its  thermal  conductivity.  The  three  values 
agree  among  themselves  as  well  as  could  be  expected. 

Let  us  return  now  for  a  brief  space  to  our  solid 
again.  Solids  may  be  divided  into  two  classes, 
according  as  they  do  or  do  not  conduct  electricity. 
It  is  also  found  that  conductors  of  electricity  are 
also  good  conductors  of  heat,  while  electrical  insu- 
lators are  generally  very  poor  conductors  of  heat. 
We  have  by  now  come  to  connect  electricity  with 
electrons,  and  hence  an  electric  current  is  a  flow  of 
electrons  from  a  place  of  high  to  a  place  of  low 
potential.  We  may  regard  a  conductor,  then, 
as  a  substance  containing  electrons  which  are  free 
to  move  under  the  action  of  an  electric  field,  while 
in  non-conductors  the  electrons  are  fixed  and  unable 
to  follow  the  impulse  of  the  field. 

How  are  these  electrons  set  free  ?  In  the  first 
place  it  may  be  noticed  that  the  only  good  con- 
ductors of  electricity  are  metallic,  that  is  to  say, 
electro-positive  in  character,  substances  which  we 
know  from  other  phenomena  readily  part  with  an 
electron  under  the  slightest  provocation.  Now  in 
a  solid  such  provocation  may  well  be  supplied  by 
the  close  propinquity  of  the  neighbouring  mole- 
cules. It  is  well  known  that  a  charged  body  will 
attract  light  uncharged  substances.  The  attraction 
of  a  well-rubbed  stick  of  sealing  wax  for  small 
pieces  of  paper  is  generally  our  first  introduction 
to  the  science  of  electricity.  The  attraction  is  of 
course  mutual,  the  force  on  the  charged  body  being 
equal  to  that  on  the  uncharged  paper.  Hence  an 
electron  in  one  atom  is  attracted  by  a  neighbouring 
uncharged  atom,  and  under  favourable  circumstances, 
and  especially  in  the  case  of  an  atom  only  too  ready 
to  part  with  its  electrons,  the  attraction  may  well 
be  sufficient  to  enable  it  to  make  its  escape; 


140  MOLECULAR   PHYSICS 

That  some  such  assistance  is  necessary  and  is 
so  given,  is  shown  by  the  fact  that  a  metallic  vapour 
is  no  better  a  conductor  than  any  other  gas  at  the 
same  temperature.  Thus  while  metallic  mercury 
at  its  boiling  point  is  an  excellent  conductor  of 
electricity,  the  mercury  vapour  above  it  conducts 
little  better  than  the  air  it  displaces,  that  is  prac- 
tically not  at  all. 

The  evolution  of  electrons  by  the  molecules  of 
a  metal  is  very  similar  to  the  evaporation  of  a  liquid 
into  a  closed  space — a  phenomenon  we  have  already 
described.  It  will  go  on  until  the  number  of 
electrons  which  are  attracted  by  the  positively 
charged  residues  and  so  recombine,  is  equal  to  the 
number  of.  electrons  which  are  given  off  by  the 
neutral  molecules  in  the  same  time.  Thus  for  a 
given  temperature  there  will  be  a  definite  pressure 
of  electrons  per  unit  volume  in  the  metal,  and  we 
may  in  fact  look  upon  the  electrons  as  a  kind  of 
tenuous  gas  filling  up  the  interspaces  between  the 
molecules  of  the  solid.  We  must  regard  them  as 
moving  about  in  all  directions  in  the  solid  with 
considerable  velocities.  The  principles  of  thermo- 
dynamics would  lead  us  to  imagine  that  when 
equilibrium  is  established  each  of  these  electrons 
will  have  the  same  average  energy  as  the  molecules 
around  it,  that  is  to  say,  the  energy  corresponding 
to  the  temperature  of  the  body  at  the  time.  This 
is  an  important  point  to  which  we  shall  return  later. 

These  electrons,  if  no  electric  force  be  acting, 
will  be  moving  in  all  directions,  so  that  if  we  take 
any  cross  section  of  the  metal  the  number  of  elec- 
trons crossing  it  in  one  direction  will  be  the  same  as 
the  number  crossing  in  the  opposite  direction,  and 
so  the  total  transference  of  electricity  across  the 
section  will  be  zero. 

If,  however,  we  apply  an  electric  field  to  the  body 
there  will  be  a  force  on  each  electron  urging  it  in 


MOLECULAR  THEORY   OF  MATTER     141 

the  direction  of  the  field.  Thus  in  addition  to  the 
irregular  motion  due  to  the  heat  energy  of  the  body, 
there  will  be  a  steady  drift  of  the  electrons  as  a 
whole  in  the  direction  of  the  electric  force. 

Let  us  consider  for  the  sake  of  simplicity,  a 
regular  conductor  such  as  a  uniform  wire.  Let  us 
apply  an  electric  field  X,  to  the  wire  along  its  length. 
Then  the  force  on  every  electron  is  equal  to  X0, 
where  e  is  the  charge  on  an  electron,  and  it  can  be 
shown  that  the  average  velocity  of  the  electron 
due  to  the  electric  field  is  K.X0,  where  K  is  some 
constant  which  for  the  moment  we  will  leave 
undetermined. 

In  one  second  all  the  electrons  which  are  less 
than  v  cms.  from  a  given  cross  section  of  the  con- 
ductor will  be  forced  across  it  under  the  action  of 
the  field.  The  volume  of  this  space  is  vA.  if  A  is 
the  area  of  cross  section,  and  thus  if  there  are  N 
electrons  per  unit  volume,  each  carrying  a  charge  e 
the  total  charge  passing  through  the  given  cross 
section  will  be  N<?.vA  units  per  second.  But  this 
is  by  definition  the  current  along  the  conductor. 
Hence  remembering  that  the  velocity  v  is  K.X0  we 
have  the  current  i  is  equal  to  K.#2N.A.X. 

If  d  is  the  length  of  the  wire  and  E  the  difference 
of  potential  between  its  ends,  the  field  X  in  the 
wire  is.  equal  to  E/d.  Hence  finally 

i  =  (K.£2N)^.  E. 
ct 

The  current  through  a  given  conductor  is  thus 
directly  proportional  to  the  difference  of  potential 
between  its  ends  which  is  the  well  known  law  of 
Ohm.  We  see  that  it  is  also  proportional  to  the 
cross  section  of  the  conductor,  and  inversely  pro- 
portional to  its  length.  We  may  thus  write  it 


where  a-  is  written  for  the  quantity  in  the  bracket. 


142  MOLECULAR  PHYSICS 

This  is  a  well-known  expression  for  the  current 
through  a  wire.  The  quantity  o-  which  is  a  con- 
stant for  a  given  substance  at  a  given  temperature, 
is  known  as  its  specific  electrical  conductivity.  Com- 
paring the  equations  we  see  that  the  conductivity  a 
is  equal  to  K.e^N. 

Now  the  constant  K  can  be  evaluated  on  certain 
probable  assumptions  and  has  been  shown  to  be 
equal  to  V  A/6  RT,  where  V  is  the  velocity  of  the 
turbulent  motion  of  the  electrons,  A  is  the  average 
distance  traversed  by  the  electron  between  one 
collision  with  a  molecule  and  the  next,  R  is  the 
well  known  constant  from  the  gas  equation,  and  T 
is  the  temperature  of  the  conductor  on  the  absolute 
scale.  Hence  finally  the  electrical  conductivity  of 
a  substance  is  given  by  the  expression 

N  e*  A  V 
6.R.T. 

This  relation  contains  several  quantities  which 
are  at  present  unknown  to  us,  and  so  we  cannot 
put  it  directly  to  the  test.  Let  us  proceed,  however, 
a  little  further. 

Suppose  now  that  instead  of  applying  an  electric 
field  to  the  metal,  we  begin  to  heat  one  end  of  it. 
We  have  seen  that  the  turbulent  velocity  of  the 
electrons  depends  only  on  the  temperature,  and 
hence  the  electrons  in  contact  with  the  heated  area 
will  begin  to  move  with  a  greater  speed  than  those 
in  the  colder  parts  of  the  substance.  These  elec- 
trons are  moving  in  all  directions,  and  so  in  course 
of  time,  some  will  move  away  into  the  colder 
regions,  carrying  their  increased  velocity  with  them. 
Their  places  near  the  hot  end  will  of  course  be 
taken  by  electrons  from  the  colder  parts  which  in 
turn  will  have  their  motion  accelerated  by  contact 
with  the  hot  face. 

Thus  there  will  be  a  constant  stream  of  quickly 


MOLECULAR  THEORY   OF  MATTER     143 

moving  electrons  from  the  hot  end  into  the  cold 
parts  of  the  body,  sharing  their  energy  with,  and 
thus  increasing  the  velocity  of,  the  molecules 
there.  But  the  temperature  at  any  point  in  the 
body  depends  only  on  the  speed  with  which  the 
particles  are  moving.  Thus  to  translate  the  pro- 
cess from  molecular  to  molar  physics,  heat  has  been 
conducted  from  the  hot  to  the  cold  parts  of  the  body, 
and  the  rate  at  which  this  process  takes  place 
measures  what  is  called  the  thermal  conductivity 
of  the  substance. 

Since  then  the  free  electrons  play  the  principal 
role  both  in  the  conduction  of  electricity,  and  the 
conduction  of  heat  we  should  expect  to  find  some 
sort  of  relation  between  the  conductivity  of  a  sub- 
stance for  heat  and  its  conductivity  for  electricity. 

It  has  long  been  known  that  good  conductors 
of  the  one  are  also  good  conductors  of  the  other, 
and  as  long  ago  as  the  middle  of  last  century, 
Wiedemann  and  Franz,  by  comparing  the  experi- 
mental results  for  a  number  of  metals,  discovered 
that  the  ratio  of  the  thermal  to  the  electrical 
conductivity  had  the  same  value  for  all  metallic 
substances.  Somewhat  later  Lorenz,  by  making 
the  comparison  at  different  temperatures,  found 
that  the  magnitude  of  this  ratio  was  simply  propor- 
tional to  the  temperature  at  which  the  comparison 
was  made,  reckoned  from  the  absolute  zero  of  tem- 
perature. These  results  are  well  brought  out  in 
Table  X.  The  second  column  gives  the  ratio  of 
the  thermal  to  the  electrical  conductivities  at 
18°  C.  for  the  metals  given  in  the  first  column  of  the 
table.  The  last  column  gives  the  observed  tem- 
perature coefficient  of  the  ratio.  If  Lorenz'  law  is 
true,  this  coefficient  should  have  the  value  '00366. 

For  many  years  this  empirical  law  of  Wiedemann 
and  Franz  remained  without  explanation.  The 
electron  theory  of  conduction  would,  however,  as 


144 


MOLECULAR   PHYSICS 


we  have  seen,  lead  us  to  expect  with  confidence 
some  such  relationship.  We  can,  however,  go  further 
than  this.  We  have  already  seen  how  to  calculate 
the  electrical  conductivity  of  a  metal.  Its  thermal 
conductivity  can  also  be  calculated  if  we  assume 
that  the  heat  is  all  carried  by  electrons.  This 
assumption  cannot  be  strictly  true,  bscause  sub- 
stances which  are  non-conductors  of  electricity 
still  conduct  heat  to  a  small  but  finite  degree.  In 
this  case  the  transference  of  heat  is  carried  on  by  the 
molecules  themselves,  the  heated  molecules  trans- 

TABLE  X. 


Ratio  of  Thermal 

Temperature 

Metal. 

to  Electrical 

Coefficient  of  the 

Conductivity. 

Ratio. 

Copper  . 

6'7I    X    IO10 

•0039 

Silver    . 

6-86  X  io10 

•0037 

Gold      . 

.. 

7-09  x   io10 

•0037 

Nickel  . 

'      .     ": 

6*99  X   io10 

•0039 

Zinc 

6-72  X   io10 

•OO^S 

Cadmium 

7'o6  X   io10 

•0037 

Lead     . 

7*15  X   io10 

•0040 

Tin 

7-35  X  io10 

•0034 

Platinum 

7*53  X  io10 

•0046 

i 

ferring  their  increased  velocity  to  their  immediate 
neighbours  by  the  somewhat  tedious  process  of 
repeatedly  bumping  against  them.  This  method 
is  necessarily  slow  compared  to  that  of  the  freely 
moving  electrons,  and  the  very  small  thermal  con- 
ductivities possessed  by  electrical  insulators  leads 
us  confidently  to  suppose  that  the  amount  of  heat 
transmitted  in  this  way  in  a  metallic  conductor  is 
very  small,  compared  with  that  carried  by  the 
electrons. 

The  free  electrons  in  a  metal  behave,  as  we  have 
seen,  like  a  rarefied  gas.     We  can  therefore  apply 


MOLECULAR  THEORY   OF  MATTER    145 

the  results  obtained  for  gases  to  them.  The  thermal 
conductivity  of  a  gas  has  been  worked  out  by  Max- 
well and  others.  The  mathematical  analysis  of  the 
problem  would  lead  us  too  far.  It  is  contained  in 
all  treatises  on  the  dynamical  theory  of  gases.  It 
is  found  that  the  thermal  conductivity  of  a  gas  is 
represented  by 

|N  A  V.R 

where  N,  A,  V,  and  R  have  the  same  meaning  as  in 
the  equation  for  electrical  conductivity. 

Hence  comparing  the  two  equations  we  have  — 


Thermal  conductivity       .  i  /AJ\  vi^ 
Electrical  conductivity  ~  6  R.T 


This  is  a  very  simple  relation  indeed.  All  the 
quantities  with  which  we  are  unfamiliar  have  gone 
out,  leaving  only  R  the  constant  of  the  gas  equation, 
e  the  ubiquitous  electronic  charge,  and  T  the  tem- 
perature on  the  absolute  scale  at  which  our  com- 
parison is  made.  Let  us  substitute  for  these  symbols 
their  numerical  values,  and  so  bring  our  theory  to 
a  critical  numerical  test.  R  in  absolute  units  is 
equal  to  1*40  X  io~16,  while  e  in  electro-magnetic 
units  is  1-57  X  io~20.  If  the  comparison  is  made 
at  18°  C.,  as  in  Table  X.,  T  is  (18°  +  273°)  or  291° 
on  the  absolute  scale. 

Hence,  the  ratio  of  the  two  conductivities  should 
be  equal  to  —  • 

3  X  ^  ><  ™~Z  X  29I, 

(1-57  x  lo-20)2 

or  6-95  X  io10. 

The    agreement   with   the   experimental   values 
given  in  Table  X.  is  satisfactory  beyond  the  bounds 
of  expectation.     Since  R  and  e  are  both  independent 
M.P.  io 


146  MOLECULAR   PHYSICS 

of  the  temperature  it  is  evident  from  our  equation, 
that  the  ratio  varies  directly  as  the  absolute  tempera- 
ture as  was  discovered  experimentally  by  Lorenz. 

The  electron  theory  of  conduction  has  many 
other  triumphs  and  at  present  also  not  a  few  unsolved 
difficulties,  which  would  need  a  treatise  rather  than 
a  chapter  to  expound.  Let  us,  therefore,  leave  the 
subject  here,  and  take  a  final  and  farewell  glance  at 
our  atom,  this  time  in  the  throes  of  dissolution. 


CHAPTER   IX. 

THE  ATOM  IN  DISSOLUTION. 

IF  the  ideas  which  have  been  developed  in  the 
preceding  chapters  have  any  sort  of  foundation  in 
fact,  the  title  of  the  present  chapter  will  hardly 
come  as  a  shock  to  any  reader.  It  may  seem  at 
first  sight  much  more  surprising  that  a  system  s"o 
complex  as  the  one  we  have  described,  and  in  such 
constant  motion,  when  subjected  to  all  the  shocks 
mechanical,  chemical,  and  electrical,  which  an 
atom  must  undergo,  should  continue  to  exist  in  such 
a  persistent  and  unchangeable  way  as  is  actually 
found  to  be  the  case. 

The  cause  is  probably  to  be  found  in  the  rela- 
tively enormous  amount  of  energy  associated  with 
an  atom,  an  amount  which  is  quite  out  of  proportion 
to  the  energy  liberated  by  chemical  reactions.  It 
has  been  shown  that  the  heat  liberated  by  the 
transformation  of  one  gram  of  radium  into  its 
final  product  is  about  4  X  io9  gram  calories.  Com- 
pared with  this  enormous  quantity  the  heat  liberated 
in  the  most  energetic  of  chemical  reactions  fades 
into  insignificance.  The  formation  of  a  gram  of 
water  for  example,  is  attended  by  the  emission  of 
about  4  x  io3  gram  calories.  And  yet  this  enor- 
mous quantity  must  only  be  a  small  fraction  of 
the  total  energy  in  the  radium  atom.  Radium, 
as  we  shall  see,  has  an  atomic  weight  of  225  ;  the 
final  product  of  its  decomposition  one  of  about  206. 
This  atom,  whatever  it  may  be  (modern  speculation 

IO — 2 


148  MOLECULAR   PHYSICS 

points  to  lead,  but  the  proof  is  far  from  complete) 
is  stable  and  must  possess  a  very  large  amount  of 
energy  of  its  own.  The  total  energy  in  an  atom 
must  therefore  be  enormous,  and  it  is  for  this  reason 
that  all  efforts  to  transmute  one  element  into 
another  have  failed. 

Great  as  this  energy  is,  however,  our  theory 
indicates  that  there  is  a  steady  and  continuous 
drain  upon  it  which  sooner  or  later  must  bring 
about  instability,  and  the  dissolution  of  the  system. 
We  saw  in  the  last  chapter  that  an  electron  in  motion 
round  a  circle  is  a  source  of  radiation.  The  rate  of 
radiation  depends  on  several  factors.  A  single 
electron  moving  in  a  circle  is  a  very  efficient  radiator, 
and  would  quickly  drain  any  atom  of  its  enormous 
supply.  It  can  be  shown,  however,  that  if  several 
electrons  are  moving  round  the  same  circle  the 
amount  of  radiation  is  very  considerably  reduced, 
so  that  for  a  continuous  ring  of  electrons  the  effect 
would  be  very  small  indeed.  Small  or  great, 
however,  it  is  a  constant  source  of  loss  which  in 
the  course  of  ages  must,  in  the  absence  of  some 
counteracting  force  with  which  we  are  at  present 
unacquainted,  bring  about  the  downfall  of  the 
atom. 

It  is  doubtful  how  far  this  deduction  and  the 
theory  on  which  it  is  based  would  have  found  any 
acceptance  had  it  not  been  for  the  discovery,  almost 
simultaneously  with  the  rise  of  the  electron  theory, 
of  a  series  of  phenomena  which  found  in  it  their 
only  possible  explanation. 

The  main  outlines  of  the  new  science  of  radio- 
activity are  perhaps  familiar  to  all  readers.  The 
subject  is  one  of  profound  interest,  but  it  lies  almost 
wholly  outside  the  scope  of  such  a  work  as  this. 
We  will,  however,  summarise  such  of  the  main  facts 
of  that  science  as  bear  on  our  immediate  subject, 
leaving  the  proof  of  the  various  statements  and  the 


THE  ATOM   IN   DISSOLUTION         149 

description  of  the  often  very  beautiful  experiments 
from  which  they  were  deduced  to  other  hands. 

The  metal  uranium  and  its  compounds  were 
found  by  Becquerel  to  give  off  continuously  par- 
ticles capable  of  affecting  a  photographic  plate  at 
a  considerable  distance.  These  are  the  /3-rays 
which,  as  was  mentioned  in  an  earlier  chapter,  are 
identical  except  in  speed  with  the  cathode  rays. 

If  the  uranium  salt  is  subjected  to  certain 
chemical  processes  it  is  possible  to  separate  the 
uranium  compound  into  twro  fractions.  In  one 
fraction,  an  almost  imperceptible  part  of  the  whole, 
all  the  power  of  emitting  /3-rays  is  concentrated. 
The  other,  containing  practically  all  the  original 
salt,  is  completely  inactive.  For  example,  if  we 
follow  Sir  William  Crookes  and  shake  up  crystals  of 
uranium  nitrate  in  ether,  the  water  of  crystalliza- 
tion, which  settles  out  beneath  the  ethereal  solution 
and  can  be  separated  from  it  by  a  separating  funnel, 
is  found  to  contain  by  far  the  greater  part  of  the 
/3-ray  activity  of  the  whole,  the  great  mass  of  the 
salt  now  dissolved  in  the  ether  being  comparatively 
inactive. 

Let  us  take  these  two  solutions  and  keep  them 
under  observation  for  some  time.  It  will  be  noticed 
that  the  watery  solution  is  gradually  losing  its 
/3-ray  producing  powers,  the  rate  of  emission  of 
these  rays  falling  in  fact  to  half  its  original  value  in 
about  twenty-five  days.  At  the  same  time  the  ethereal 
solution  which  we  had  rendered  inactive,  gradually 
begins  to  radiate  again,  so  that  at  the  end  of  twenty- 
five  days  it  has  recovered  one-half  of  its  original 
activity.  Fig.  29  shows  in  a  graphic  way  the  exact 
correlation  between  the  loss  of  radio-activity  by  the 
active  fraction  and  the  growth  of  activity  in  the  in- 
active mass.  It  will  be  seen  that  the  total  activity  is 
constant  throughout  the  experiment.  From  these 
results  we  may  draw  the  following  conclusions. 


150 


MOLECULAR  PHYSICS 


In  the  first  place,  the  property  of  ejecting  these 
electrons  with  enormous  speeds  resides  not  in  the 
uranium  itself,  but  in  some  substance  which  is  mixed 
with  it  but  which  can  be  separated  from  it  by 
suitable  chemical  processes.  Secondly,  this  sub- 
stance is  not  a  stable  substance  but  loses  its  'activity 


FIG.  29. — Growth  and  decay  of  $-ray  activity  with  time  for 
uranium  and  uranium  X. 

with  time.  Lastly,  this  substance  is  not  of  the 
nature  of  an  impurity  in  the  uranium,  but  is  so 
vitally  bound  up  with  it  that  when  the  latter  is 
completely  freed  from  its  presence  it  can  reproduce 
this  strange  substance  again  at  a  steady  and  per- 
fectly definite  rate.  The  conclusion  seems  irresistible. 


THE  ATOM   IN   DISSOLUTION         151 

Some  new  substance  is  being  produced  out  of 
uranium  itself,  and  in  turn  is  decomposing  with 
considerable  celerity  into  some  other  substance 
which  for  the  moment  we  are  unable  to  pursue. 

I  have  discussed  the  case  of  uranium  because 
that  metal  is  a  recognised  element  belonging  to  a 
well-known  and  respectable  family,  and  might  have 
been  expected  to  behave  in  a  rational  and  orthodox 
manner.  The  case  of  radium  (which  is  actually  a 
decomposition  product  of  uranium)  is  still  more 
striking.  Rutherford  discovered  that  radium  and 
its  salts  are  constantly  giving  off  a  heavy,  chemically 
inert  gas  known  as  the  "emanation,"  a  non-committal 
name  bestowed  upon  it  before  its  nature  had  baen 
determined.  This  emanation  collects  in  the  radium, 
but  can  be  extracted  from  it  by  heating  under 
reduced  pressure  or  better  still,  by  dissolving  the 
salt  in  water  and  boiling  the  solution.  In  either 
way  the  radium  can  be  completely  freed  from  this 
new  gas.  On  allowing  the  gas  and  the  radium  to 
stand,  however,  it  is  found  that  fresh  emanation 
makes  its  appearance  in  the  radium,  while  the 
collected  emanation  gradually  disappears,  the  rela- 
tion between  the  growth  and  decay  of  the  emanation 
being  precisely  similar  to  that  of  uranium  and  its 
/3-ray  producing  product.  It  is  impossible  to  escape 
the  conclusion  that  the  element  radium  is  evolving 
out  of  its  own  substance  the  heavy  gas  known  as 
the  emanation. 

The  properties  of  both  radium  and  its  emanation 
are  now  quite  well  known.  Radium  is  a  metal  of 
the  calcium  group,  with  an  atomic  weight  of  226*5. 
It  has  been  prepared  in  a  metallic  state,  and  its 
properties  are  found  to  agree  with  the  place  we  have 
assigned  to  it  in  the  periodic  table.  The  emanation 
on  the  other  hand  is,  as  we  have  said,  a  chemically 
inert  gas  resembling  the  members  of  the  helium 
group.  It  can  be  liquefied  at  —150°  C.  Sir  William 


152 


MOLECULAR  PHYSICS 


Ramsay  has  even  succeeded  in  determining  its 
density,  an  achievement  which  as  a  triumph  of  skill 
and  refinement  of  experimental  method  is  beyond 
all  praise.  The  difficulties  of  the  work  will  be 
realised  when  it  is  mentioned  that  the  total  volume 


TABLE  XI. 


Element.                                 Average  Life. 

Rays  emitted. 

Uranium 

1 
Uranium  X 

1 

238-5 
(230*5) 

6  x  io9  years 
24*6  days 

a,  a 

P.  y 

Ionium 

i 

Radium 

i 

230*5 
226*5 

200,000  years 
2,000  years 

a 
a 

Emanation 

1 
Radium  A 

i 

223 

(222-5) 
(218-5) 

3*85  days 
•3  minutes 

a 
a 

Radium  B 

i 

(214*5) 

26*8  minutes 

none 

Radium  C 

(214*5) 

19-5  minutes 

«,  ft  7 

i 

Radium  D 

i 

(210-5) 

40  years 

none 

Radium  E 

i 

(210-5) 

4*8  days 

£ 

Polonium 

! 

(210-5) 

140  days 

a 

?' 

(206-5) 

'  — 

— 

of  emanation  available  for  the  determination  was 
less  than  one-tenth  of  a  cubic  millimetre. 

The  molecular  weight  of  the  emanation  deduced 
from  this  determination  is  223.  Assuming  the 
gas  to  be  monatomic  like  the  gases  it  most  resembles, 
this  is  also  its  atomic  weight. 

What  happens  to  that  fragment  of  the  radium 


THE  ATOM  IN  DISSOLUTION         153 

atom  which  represents  the  difference  between 
226*5,  the  atomic  weight  of  radium,  and  223,  that  of 
its  emanation  ?  The  answer  is  not  far  to  seek.  It 
will  be  remembered  that  radium  is  constantly 
giving  off  what  are  known  as  a-rays  which,  as  we 
saw  in  an  earlier  chapter,  have  been  proved  to  be 
helium  atoms  with  a  high  velocity  and  an  electric 
charge.  The  atomic  weight  of  helium  is  4-0. 
Within  the  limits  of  experimental  error  this  is  the 
difference  between  the  weight  of  an  atom  of  radium 
and  that  of  the  emanation. 

The  break  up  of  the  radium  atom  therefore 
takes  place  as  follows.  Its  energy  content  becomes 
too  small  for  its  mass  and  a  small  fragment  of  it 
which  we  must  regard  as  having  been  whirling  round 
in  the  atom  with  a  great  velocity,  is  projected  like 
a  stone  from  a  sling,  or  rather,  like  one  of  the 
fragments  of  a  bursting  flywheel.  This  fragment 
is  always  an  atom  of  helium — why,  we  do  not  know. 
The  residue  of  the  atom,  its  atomic  weight  now 
reduced  by  four,  forms  a  new  substance,  which  in 
this  case  happens  to  be  gaseous. 

The  emanation  itself  is  very  far  from  being 
stable.  It  is  half  decomposed  in  a  little  less  than 
four  days,  the  new  decomposition  product  being 
in  this  case  a  solid.  We  cannot  follow  here  the 
changes  undergone  by  the  atom  in  its  attempts  to 
reach  a  stable  state.  They  are,  however,  sum- 
marised in  Table  XL,  which  gives  at  a  glance  the 
whole  of  the  interesting  but  pitiful  story  from  the 
break  up  of  the  original  uranium  atom  to  that  of 
polonium,  the  last  member  of  the  chain  to  be 
definitely  identified. 

The  first  column  gives  the  name  of  the  element, 
and  its  probable  atomic  weight.  Those  enclosed 
in  brackets  have  not  been  actually  determined,  but 
are  deduced  on  the  assumption  that  each  emission 
of  an  a-particle  involves  a  loss  of  atomic  weight  of 


154  MOLECULAR  PHYSICS 

four  units.  The  second  column  gives  the  time  taken 
for  the  element  to  lose  one-half  of  its  mass,  or  in 
other  words  for  one-half  of  its  atoms  to  decompose. 
It  may  be  called  the  average  life  of  the  atoms  of 
the  element.  The  third  column  indicates  the  nature 
of  the  rays  emitted  by  the  substance  on  its  decom- 
position. 

Polonium  itself  is  radio-active,  but  its  decompo- 
sition product  has  not  yet  been  identified.  The 
worn  out  atom  has  probably  found  peace  at  last, 
and  hence  no  longer  emits  those  radiations  which 
in  most  cases  afford  our  only  means  of  following 
its  changes.  It  will  be  seen  from  the  table  that 
five  a-particles  are  given  out  in  the  passage  from 
radium  to  this  final  product.  If  each  of  these  is  a 
helium  atom  the  atomic  weight  of  the  final  element 
should  be  226-5  —  (5  x  4)  or  206-5.  This  is  very 
approximately  the  atomic  weight  of  lead,  and  it 
has  been  conjectured  with  some  degree  of  proba- 
bility that  lead  is  the  final  stable  product  of  this 
great  series  of  changes.  At  present,  however,  the 
evidence  can  hardly  be  said  to  amount  to  a  proof. 

Most  of  these  radio-active  changes,  as  they  are 
called,  result  in  the  expulsion  of  an  a-particle,  and 
consequent  change  in  atomic  weight.  Others, 
however,  for  example,  that  of  Uranium  X,  the  decom- 
position product  of  uranium  with  which  we  com- 
menced our  survey  of  the  subject,  give  off  only 
/3-particles,  and  hence  differ  inappreciably  in  atomic 
weight  from  their  immediate  successor.  The  7-rays 
which  always  accompany  /3-radiation  are  merely 
electro -magnetic  pulses  due  to  the  sudden  ejection 
of  the  negatively  charged  particles,  and  do  not 
concern  us  here.  In  some  cases,  there  is  apparently 
no  emission  of  any  kind  of  radiation  by  the  atom, 
the  change  in  this  case  consisting  of  a  mere  re- 
arrangement of  the  electrons  within  the  atom  itself. 

So  far  we  have  been  treading  on  safe  ground. 


THE  ATOM   IN   DISSOLUTION         155 

There  can  be  no  doubt  that  the  scheme  we  have 
outlined  so  briefly  above  represents  the  true  relation 
between  the  various  radio-active  substances.  The 
disintegration  theory  which  is  due  to  the  genius  of 
Professor  Rutherford,  as  much  of  the  work  embodied 
in  the  table  is  due  to  his  experimental  skill  and 
energy,  is  the  only  theory  which  can  in  any  xway 
explain  this  novel  series  of  facts.  It  is  now  univer- 
sally accepted.  It  is  when  we  come  to  consider  the 
mechanism  of  the  change  that  difficulties  arise. 

Of  actual  knowledge  we  can  hardly  be  said  to 
have  any,  but  something  may  be  conjectured.  We 
saw  that  the  rings  of  electrons  of  which  we  built  up 
the  atom  were  in  many  cases  only  stable  if  they 
were  revolving  round  the  atom  with  a  velocity 
exceeding  a  certain  critical  value.  Owing  to  radia- 
tion from  the  system  the  velocity  of  the  electrons 
must  be  gradually  but  constantly  decreasing,  and 
a  time  must  come  when  it  will  be  insufficient  to 
ensure  stability. 

It  seems  probable  that  when  this  stage  is  reached 
one  of  the  electrons  leaves  the  ring  and  commences 
an  orbit  on  its  own  account.  The  radiation  from  a 
single  electron,  is  however,  very  much  greater  than 
from  a  number  of  electrons  moving  in  the  same 
orbit,  and  the  loss  of  energy  from  the  atom  is 
greatly  increased.  This  brings  about  a  state  of 
instability  which  results  in  the  expulsion  of  an 
a-particle  or  helium  atom,  though  why  the  expulsion 
should  always  take  this  form  is  a  question  we  are 
far  from  having  solved.  In  some  cases  the  breaking 
off  of  this  positive  portion  enables  the  atomic  forces 
to  expel  the  disturbing  /3-particle,  in  which  case 
there  is  at  any  rate  a  temporary  lull  in  the  pro- 
ceedings. In  other  cases,  as  in  that  which  follows 
the  break  up  of  the  radium  atom,  four  helium  atoms 
are  ejected  in  quick  succession,  one  of  the  stages 
lasting  only  three  minutes,  until  finally  radium  C 


156  MOLECULAR   PHYSICS 

expels  the  disturbing  electron,  and  the  succeeding 
element  radium  D  enjoys  an  average  life  of  forty 
years. 

Whether  this  account  is  correct  or  no,  there  is 
distinct  evidence  that  it  is  the  /3-particle  which  is 
the  disturber  of  the  atomic  peace  for  in  every  case 
the  expulsion  of  a  /3-particle  seems  to  bring  about 
an  increase  in  the  stability  of  the  system,  the  suc- 
ceeding change  having  a  much  longer  half  period 
than  the  changes  immediately  preceding  it. 

The  subject  is  one  full  of  difficulties,  but  where  so 
much  has  been  done  we  may  well  expect  still  more. 
We  are  marching  with  a  triumphant  army,  and  are 
not  inclined  to  set  any  bounds  on  the  extent  of  our 
possible  conquests  in  the  future. 

In  addition  to  the  radium-uranium  series,  two 
other  elements,  thorium  and  actinium  are  strongly 
radio-active,  giving  rise  to  series  of  decomposition 
products,  similar  to  the  chain  we  have  already 
considered.  The  question  now  arises,  are  all  the 
elements  suffering  from  this  slow  decay,  or  are  these 
few  heavy  elements  alone  in  their  spontaneous 
decomposition  ? 

Extensive  researches  have  been  made  to  answrer 
this  question,  but  the  results  are  perhaps  not  quite 
as  definite  as  might  be  desired.  Potassium  has  been 
found  to  give  off  appreciable  quantities  of  /3- 
radiation,  its  activity  in  this  respect  being  about  i% 
of  that  of  uranium.  Its  radio-activity,  if  such  it 
is,  seems  to  be  of  a  peculiar  kind,  as  in  spite  of  very 
prolonged  and  drastic  experiments,  both  by  Camp- 
bell who  discovered  the  phenomenon,  and  by  others, 
it  has  not  been  found  possible  to  separate  from  the 
potassium  any  substance  bearing  the  same  relation 
to  the  potassium  as  Uranium  X  bears  to  uranium. 
Rubidium  and  possibly  caesium  show  similar  effects. 

With  all  other  elements  the  effect,  if  it  exists, 
is  very  small.  There  is,  however,  considerable 


THE  ATOM   IN  DISSOLUTION         157 

evidence  for  the  radio-activity  of  all  kinds  of  matter, 
although  it  hardly  amounts  to  a  formal  proof. 

If  we  examine  a  quantity  of  air  enclosed  in  a 
metal  vessel  we  find  that,  even  in  the  absence  of 
any  specific  ionizing  agent  a  certain  number  of 
ions  are  always  being  formed  in  the  air,  which 
enable  us  to  send  a  small  but  measurable  current 
through  the  air.  It  has  been  shown  that  a  great 
part  of  this  ionization  is  due  to  radium  which 
disseminated  through  the  atmosphere  as  emanation, 
or  present  in  solid  form  in  the  soil,  seems  to  be  quite 
ubiquitous.  It  is  found,  however,  that  the  amount 
of  this  ionization  depends  on  the  substance  of  which 
the  walls  of  the  vessel  are  made,  it  is  for  example, 
greater  in  a  lead  than  in  a  copper  vessel.  This 
would  certainly  seem  to  point  to  the  emission  from 
the  walls  themselves  of  an  ionising  radiation  of 
some  sort,  which  is  greater  in  amount  for  lead  than 
for  copper. 

The  matter  is  complicated  by  the  fact  that  a 
certain  amount  of  secondary  radiation  is  set  up 
when  radium  rays  impinge  on  various  metals,  and 
these  might  very  well  depend  for  their  intensity  on 
the  nature  of  the  metal  used.  Dr.  N.  R.  Campbell 
who  has  made  this  subject  his  own,  decides  against 
this  explanation.  I  cannot  do  better  than  quote 
his  deliberate  conclusions. 

"  It  has  been  proved  beyond  doubt  that  the 
emission  of  ionizing  radiation  is  an  inherent  pro- 
perty of  all  the  metals  investigated.  It  is  not  of 
course  necessary  that  this  ray  emission  should  be 
identified  at  once  with  radio-activity — if  that  word 
is  taken  to  mean  a  process  of  ray  emission  accom- 
panied by  atomic  decomposition.  But  the  constant 
intensity  of  the  rays,  and  the  probability  that  the 
larger  portion  of  them  are  a-rays,  afford  considerable 
support  for  that  hypothesis  ;  while  I  know  of  no 
other  process  which  affords  any  analogy/' 


158  MOLECULAR   PHYSICS 

The  process  is  not  proceeding  at  such  a  rate  as 
to  give  cause  for  legitimate  alarm.  As  we  have 
seen,  the  aveiage  life  of  a  uranium  atom  is  about 
six  thousand  million  years  ;  from  a  comparison  of 
the  relative  intensities  of  the  radiation  from  uranium 
and  from  ordinary  materials  we  may  conclude  that 
the  average  existence  of  the  latter  cannot  be  less 
than  ten  thousand  times  longer  still.  If,  however, 
we  accept  Dr.  Campbell's  conclusion  that  all  sub- 
stances are  emitting  a-particles  then,  whether 
quickly  or  slowly,  all  matter  is  in  the  process  of 
gradual  dissolution  into  helium,  and  perhaps 
hydrogen. 

It  is  curious  that  in  this  case  the  conclusions  to 
be  drawn  from  a  sister  science,  that  of  astronomical 
physics,  diametrically  contradict  those  which  we 
have  arrived  at  from  a  consideration  of  radio- 
activity. It  is  a  well-known  fact  that  the  very 
hottest  and  therefore  presumably  the  newest  stars, 
when  examined  by  the  spectroscope  are  seen  to 
consist  of  very  little  else  than  hydrogen,  helium, 
and  two  other  elements,  the  spectra  of  which  have 
not  yet  been  identified  on  the  earth.  Coming  to 
some  of  the  slightly  cooler  stars  fresh  elements  all 
of  low  atomic  weight  gradually  make  their  appear- 
ance, the  list  increasing,  and  elements  of  higher 
and  higher  atomic  weight  coming  into  existence 
as  cooler  and  cooler  stars  are  examined.  As  we 
have  no  reason  whatever  to  suppose  that  the  uni- 
verse was  anything  save  homogenous  in  the  begin- 
ning, we  are  led  to  the  conclusion  that  all  the  ele- 
ments as  we  have  them  on  this  earth  are  in  reality 
aggregates  of  hydrogen,  helium,  and  these  two 
unknown  elements. 

In  these  stars  progress  is  obviously  from  the 
simple  to  the  complex.  Little  by  little  new  elements 
are  created  by  the  gradual  aggregation  of  the  lighter 
atoms.  Oil  earth,  so  far  as  we  can  follow  it  the 


THE  ATOM   IN   DISSOLUTION          159 

change  is  in  the  opposite  direction,  the  heavier  atoms 
such  as  uranium  and  thorium  spontaneously  breaking 
down  into  simpler  and  simpler  systems.  It  must  be 
remembered  that  so  far  as  we  know  the  decomposi- 
tion of  the  radio-active  elements  is  quite  uninfluenced 
by  any  change  of  conditions  which  can  be  applied 
to  them.  The  substance  can  be  heated  up  in  the 
electric  furnace  or  cooled  to  the  temperature  of 
liquid  hydrogen  without  in  anyway  altering  its  slow 
but  steady  rate  of  decomposition.  It  is  true  that 
the  highest  temperatures  which  we  can  attain  are 
small  compared  with  those  of  the  hotter  stars,  but 
it  is  difficult  to  conceive  that  a  rise  in  temperature 
should  assist  aggregation,  its  tendency  being  always 
in  the  direction  of  disintegration. 

The  question  suggests  itself,  are  the  elements 
as  we  know  them  merely  a  part  of  a  great  cycle  of 
growth  and  decay  ?  Is  the  atom  born,  to  grow  old, 
decay,  and  die  ?  Are  new  atoms  being  formed  in 
the  secret  places  of  the  universe  to  take  the  place 
of  those  that  have  passed  away  ?  The  facts  have 
been  briefly  stated  above,  but  of  explanation  there 
appears  at  present  to  be  none.  We  are  brought 
not  for  the  first  time  to  one  of  those  mysteries 
which  science  has  so  far  failed  to  illuminate. 

We  have  weighed  and  measured  the  atom  ;  we 
have  analysed  it  and  learned  something  of  the 
stuff  of  which  it  is  made  and  a  little  of  its  inner 
structure,  and  the  way  in  which  it  behaves.  We 
have  now  watched  its  dissolution  and  attended  its 
obsequies.  Whether  it  will  ever  be  granted  to  us 
to  sit  as  spectators  at  a  new  birth  time  alone  can 
show. 


APPENDICES 

APPENDIX    A. 

(See  page  48.) 

DEFLECTION  OF  THE  POSITIVE  RAYS  BY  ELECTRO- 
STATIC AND  MAGNETIC  FIELDS. 

(i)  Electrostatic  Deflection. 

Let  d  be  the  length  of  the  path  of  the  particles 
over  which  the  field  is  applied,  and  D  the  distance 
of  the  photographic  plate  Z  (Fig.  9)  from  the  centre 
of  the  field  MN.  In  the  apparatus  used  d  is  small 
compared  with  D. 

Since  the  field  is  uniform  the  particle  is  acted 
upon  by  a  force  X.E,  and  acquires  an  acceleration 
XE/m  in  a  direction  perpendicular  to  its  initial 
velocity.  This  acts  for  the  time  t  taken  by  the 
particle  to  describe  the  path  d,  that  is  for  a  time  d/v. 
Hence  velocity  vr  acquired  under  the  action  of  the 
field  ' 

d 


'  m  m    '  v' 

The  particle  describes  the  remainder  of  its  path 
from  the  field  to  the  plate  under  these  two  velocities. 
Hence  the  deflection  x  is  to  the  horizontal  distance 
travelled  D  as  the  acquired  velocity  vr  is  to  the  initial 
velocity  v  of  the  particle.  Thus 

*  =  *  =  XE  d 
D       v        m   i? 


APPENDICES  161 

~      .    XE 

x  —  D  .  d  .  — s. 

mv2 

(2)  Magnetic  Deflection. 

The  path  of  the  rays  in  the  field  is  bent  into  the 
arc  of  a  circle  of  radius  r  where  r  = 


H.E' 

On  leaving  the  field  the  particles  continue  to 
move  along  the  tangent  to  this  circle  at  the  point 
where  the  field  ends.  Hence  the  angular  deflection 
6  of  the  beam  is  the  angle  between  the  tangents  to 
this  circle  where  the  path  enters  and  leaves  the  field 
respectively.  This  is  obviously  the  same  as  the 
angle  between  the  normals  to  the  circle  at  those 
points. 

Hence,  if  d  is  small  compared  with  r,  as  is  the 
case  in  practice,  we  have 

d       ,    HE 

-  =  d  .  -—. 
r  mv 

But,  if  y  is  the  deflection  as  measured  on  the 
photographic  plate, 


.. 

D  mv 

Hence 

T^     * 
y  =  D  .  d  . 


mv 


APPENDIX    B. 

(See  page  69.) 
ELECTRO-MAGNETIC  MASS  OF  AN  ELECTRON. 

With  the  electron  as  centre  describe  two  spheres 
of  radius,  r  and  r  +  dr,  and  draw  two  radii  making 

M.P.  II 


APPENDICES 

angles  0  and  0  +  d6  with  the  direction  of  motion. 
If  these  radii  are  supposed  rotated  about  the  direc- 
tion of  motion  of  the  electron,  they  will  sweep  out  a 
hollow  cone,  cutting  from  the  sphere  of  radius  r  a 
circular  zone,  the  area  of  which  is 

277?-  sin  0  .  rd0. 

The  volume  of  the  space  included  between  the 
two  spheres  and  the  hollow  cone  is  thus 

27iT2  sin  0  d0  .  dr. 

The  magnetic  field  due  to  the  moving  electron 
is  obviously  constant  throughout  the  annular  space 
so  defined  and  equal  to 

ev  sin  0 


The  energy  of  the  magnetic  field  in  the  space  is  thus 

^l  .  ^  sin  d  de  .  dr>  or  ew^ede.dr 

O7JT  ^ 

Hence  the  total  magnetic  energy  in  the  space 
between  the  two  spheres  is 

eW  sin3  6,  eWdr 

4r-2     .dr.d0=-—s-X2\ 


ev  2  2 

=  o  -^dr  -  since      sin3  0d0  =  -. 

J  .  3 

The  total  energy  in  the  field  is  therefore  the 
integral  of  this  quantity  from  the  surface  of  the 
electron  of  radius  a  to  infinity. 


APPENDICES  163 

I.e.,  total  magnetic  energy  associated  with  the 
moving  electron 


APPENDIX   C. 

THE  ZEEMAN  EFFECT. 

The  mechanical  force  on  the  rotating  electron  P 
(Fig.  25,  p.  115)  is  H.e.v,  where  H  is  the  magnetic 
field  supposed  directed  down  through  the  paper, 
e  the  charge,  and  v  the  velocity  of  the  particle.  If 
P  is  positively  charged,  it  will  act  towards  the 
centre  O,  thus  increasing  the  force  retaining  the 
particle  ;  if  negative,  it  will  oppose  it.  The 
mechanical  force  on  Q  will  obviously  be  in  the 
opposite  direction  to  that  on  P. 

Let  /be  the  retaining  force  in  the  absence  of  any 
magnetic  field.  Then,  since  the  motion  is  simple 
harmonic,  we  may  write 

f=k.r 

where  r  is  the  radius  of  the  circle  described  by  the 
particle.     Also,  by  the  laws  of  mechanics, 

mv2 

/=—  ;>          ||         |        W 

If  T  is  the  time  taken  to  complete  the  circle  once 

271T  ,    . 


V   — 

m     /4-V 


(3) 


164  APPENDICES 

Now,  if  TI,  rx,  Vi  are  the  values  of  T,  r,  and  v  for 
P  when  the  field  is  applied,  and  T2,  r2,  f  2  the  corres- 
ponding values  for  Q,  we  have 

l   forP 


forQ 

2 

where  the  charge  e  is  supposed  to  carry  its  own  sign. 
Substituting  in  these  equations  for  the  velocities 
^i  and  v2  from  (2),  and  for  k  from  (3),  and  dividing 
the  equations  by  r\  and  r2  respectively,  we  have 

4^m_4^m  27r 

qp  2     '          T^       T"  rL(^  •   T-i        '•'•-«  '•'•     '     •        V4/ 
47T2m  _  4772W  TT  277  /     \ 

":    ~r          e'  ' 


Subtracting  (5)  from  (4) 

f      I  I      ) 

~ 


„.-    f_l 
*)TI    i 

^_2rr     T2  — TI 
w  -  H  '     TjT2 

or  writing  T02  for  Ti.T2,  which  is  permissible  since 
the  change  in  the  periods  produced  by  the  magnetic 
field  is  very  small  and  T0  lies  between  TI  and  T2, 

e  _  27T  T2  —  TI 
m  ~  H      T02 

But  if  A  is  the  wave  length  of  the  light  emitted, 
and  V  is  the  velocity  of  light, 


Thus,  if  A0  is  the  original  unaltered  wave  length, 


APPENDICES  165 

Ac  that  of    the  clockwise   rotation,  \a  that  of  the 
counter-clockwise  rotation, 


6    _  2J7T        V  ~~'  V 

>»  ~~~  "H  '  ~A7~ 

V2 

277        Ac  —  \a 

—  tr  •  — n —  •  ^* 

JTl  AQ 

Thus,  if  the  particles  are  positively  charged,  the 
clockwise  rotation  will  have  the  greater  wave  length  ; 
if  negative,  the  counter-clockwise,  as  viewed  along 
the  lines  of  magnetic  force.  The  latter  is  found 
experimentally  to  be  the  case. 


TABLE  OF  ATOMIC  DATA. 

(Calculated  from  the  most  recent  observations. ) 
Mass  of  an  electron  m  8  99  x  10—28  gm. 

Charge  On  an  electron  e   }    477  X  10—  I0  e  s.  units 
or  monovalent  ion         j     1-59  x  10—  20  e  m.  units 

Ratio  of  charge  to  mass  )  1*774  X  10—  7  e.m.  units 
e/m  for  an  electron        )  per  gm. 

Radius  of  an  electron  1-87  x  10  — 13  cm. 

Electrochemical       equi-  \  >•_ 

valent    of     hydrogen  1*04  X  10^  e.m.  units 
(Mass/charge)                  )  Per  &"' 

Mass  of  a  hydrogen  atom  1*66  x  10  _  24  gm. 

Radius  of  hydrogen  atom  1-21  X  10  —  8  cm. 

Gaseous    molecules    in    \ 

i    c.c.    at   o°  C.    and       2-705  x  io4I(> 

760  mm.  pressure 

(    1-40  x  10-16  ergs,  per 
"  Gas  Constant,     R          I  degree 

Velocity  of  light,  V  2-998  x  io-\-  ™  cm.  per  sec. 


BIBLIOGRAPHY 

THE  following  brief  list  of  books  and  scientific 
papers  may  be  found  of  use  by  readers  wishing  to 
pursue  further  the  subjects  treated  of  in  the  foregoing 
pages.  It  lays  no  claim  to  completeness. 

BOOKS. 

Professor  Sir  J.  J.  Thomson's  Conduction  of 
Electricity  through  Gases,  and  Professor  Sir  E. 
Rutherford's  Radioactivity  are  the  standard  works  on 
the  physics  of  the  electron  and  on  radioactivity 
disintegration  respectively,  while  Dr.  N.  Campbell's 
Modern  Electrical  Theory  is  a  fascinating  and  original 
treatise  on  the  electron  theory  as  a  whole.  For  the 
older  kinetic  theory  of  matter,  students  cannot  do 
better  than  consult  Professor  O.  E.  Meyer's  treatise. 

The  above  books  are  of  an  advanced  character  and 
postulate  some  considerable  mathematical  and 
physical  knowledge  on  the  part  of  their  readers.  Of 
books  of  a  more  popular  type  Professor  Sir  J.  J. 
Thomson's  Electricity  and  Matter,  or  his  more  recent 
Corpuscular  Theory  of  Matter  may  be  consulted, 
while  for  a  detailed  account  of  the  experiments 
described  in  Chapter  IV.  the  same  author's  mono- 
graph on  Positive  Rays  should  be  referred  to. 

SCIENTIFIC  MEMOIRS. 

For  those  who  may  wish  to  consult  the  original 
authorities  a  list  of  a  few  of  the  most  important 
papers  is  appended. 


BIBLIOGRAPHY  167 

Sir  J.  J.  THOMSON.  "  Kathode  Rays."  Phil.  Mag., 
October,  1897.  '  The  Charge  of  Electricity 
carried  by  the  Ions  produced  by  Rontgen  Rays/' 
Phil.  Mag.,  Vol.  xlvi.,  1898.  ' 

R.  A.  MILLIKAN.  "  Charge  on  an  Electron/' 
Physical  Review,  1911.  "Elementary  Electric 
Charge/'  Physical  Review,  p.  109,  August, 

IQZS- 
C.  T.  R.  WILSON.      '  The  Photography  of  Particles 

ejected  from  Atoms/'     Proceedings  of  Royal 

Society  (Proc.  Roy.  Soc.),  A.  1913. 
E.  RUTHERFORD  and  H.  GEIGER.      '  The  Charge  and 

Nature   of    the   a-particle."      Proc.  Roy.  Soc., 

A.  1908. 
Sir  J.  J.  THOMSON.     "  Rays  of  Positive  Electricity/' 

Phil.  Mag.,  February,  1911.     Further  experi- 
ments, Phil.  Mag.,  August,  1912. 
KAUFMANN.     "  Ratio  of  Charge  to  Mass  for  High 

Speed  Electrons."     Gottingen  Nach.,  November, 

1901. 
Sir  J.  J.  THOMSON.     "  The  Structure  of  the  Atom." 

Phil.  Mag.,  March,  1904.     Phil.  Mag.,  October, 

1913.      '  The    Zeeman    Effect/'    Proc.  Camb. 

Phil.  Soc.,  Vol.  xxxix. 
E.    RUTHERFORD    and    F.    SODDY.     "  Radioactive 

Change/-'     Phil.  Mag.,  1903. 
Dr.    R.    W.    GRAY   and    Sir   W.    RAMSAY.     "The 

Density    of    Radium    Emanation."     Chemical 

News,  1911. 


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.    1  n  1^3*5 

F?EC'n  I  PI 

M/tf    10  IS* 

***«rts»  LJ    L.U 

&EC  17  is 

JCI  16  '63  -7PM 

*B  10 

10  1936 

S£P     17  J97- 

rg  >h 

f*.       4-AOO 

HOV   2  1939 

APR  10  1942.E 

AU6  27  1942 

13Mar'49PJ 

24Wa/roAV 

r 

tnivv  1  0  1954  uVi 

LD  21-100m-8,'34 

UNIVERSITY  OF  CALIFORNIA  LIBRARY 


